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Save this email address on this device (Your email address will not be added to a mailing list) Other calculators ...Free statistical calculatorsDescriptionThis procedure calculates the difference between the observed means in two independent samples. A significance value (P-value) and 95% Confidence Interval (CI) of the difference is reported. The P-value is the probability of obtaining the observed difference between the samples if the null hypothesis were true. The null hypothesis is the hypothesis that the difference is 0. Required inputFor both samples, you enter:
Computational notesThe program first calculates the pooled standard deviation s:  where s1 and s2 are the standard deviations of the two samples with sample sizes n1 and n2. The standard error se of the difference between the two means is calculated as: The significance level, or P-value, is calculated using the t-test, with the value t calculated as: The P-value is the area of the t distribution with n1 + n2 − 2 degrees of freedom, that falls outside ± t (see Values of the t distribution table). When the P-value is less than 0.05 (P<0.05), the conclusion is that the two means are significantly different. Note that in MedCalc P-values are always two-sided (or two-tailed). LiteratureHow to cite this page
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Recommended bookAn Introduction to Medical StatisticsMartin BlandBuy from Amazon This textbook is intended for medical researchers and includes the design of clinical trials and epidemiological studies, data collection, summarizing and presenting data, probability, standard error, confidence intervals and significance tests, techniques of data analysis including multifactorial methods and the choice of statistical method, problems of medical measurement and diagnosis, vital statistics, and calculation of sample size.
Enter mean, standard deviation and cutoff points and this calculator will find the area under normal distribution curve. The calculator will generate a step by stepexplanation along with the graphic representation of the area you want to find. EXAMPLES A normally distributed random variable $X$ has a mean of $20$ and a standard deviation of $4$. Determine the probability that a randomly selected x-value is between $15$ and $22$. The final exam scores in a statistics class were normally distributed with a mean of $58$ and a standard deviation of $4$. Find the probability that a randomly selected student scored more than $62$ on the exam. The target inside diameter is $50 \, \text{mm}$ but records show that the diameters follows a normal distribution with mean $50 \, \text{mm}$ and standard deviation $0.05 \, \text{mm}$. An acceptable diameter is one within the range $49.9 \, \text{mm}$ to $50.1 \, \text{mm}$. What proportion of the output is acceptable? Search our database of more than 200 calculators 228 597 806 solved problems Probability of Two EventsTo find out the union, intersection, and other related probabilities of two independent events. Please input values between 0 and 1. Probability Solver for Two EventsPlease provide any 2 values below to calculate the rest probabilities of two independent events.
Please input values between 0 and 1. Probability of a Series of Independent Events
Probability of a Normal DistributionUse the calculator below to find the area P shown in the normal distribution, as well as the confidence intervals for a range of confidence levels.
Probability of Two EventsProbability is the measure of the likelihood of an event occurring. It is quantified as a number between 0 and 1, with 1 signifying certainty, and 0 signifying that the event cannot occur. It follows that the higher the probability of an event, the more certain it is that the event will occur. In its most general case, probability can be defined numerically as the number of desired outcomes divided by the total number of outcomes. This is further affected by whether the events being studied are independent, mutually exclusive, or conditional, among other things. The calculator provided computes the probability that an event A or B does not occur, the probability A and/or B occur when they are not mutually exclusive, the probability that both event A and B occur, and the probability that either event A or event B occurs, but not both. Complement of A and BGiven a probability A, denoted by P(A), it is simple to calculate the complement, or the probability that the event described by P(A) does not occur, P(A'). If, for example, P(A) = 0.65 represents the probability that Bob does not do his homework, his teacher Sally can predict the probability that Bob does his homework as follows: P(A') = 1 - P(A) = 1 - 0.65 = 0.35 Given this scenario, there is, therefore, a 35% chance that Bob does his homework. Any P(B') would be calculated in the same manner, and it is worth noting that in the calculator above, can be independent; i.e. if P(A) = 0.65, P(B) does not necessarily have to equal 0.35, and can equal 0.30 or some other number. Intersection of A and BThe intersection of events A and B, written as P(A ∩ B) or P(A AND B) is the joint probability of at least two events, shown below in a Venn diagram. In the case where A and B are mutually exclusive events, P(A ∩ B) = 0. Consider the probability of rolling a 4 and 6 on a single roll of a die; it is not possible. These events would therefore be considered mutually exclusive. Computing P(A ∩ B) is simple if the events are independent. In this case, the probabilities of events A and B are multiplied. To find the probability that two separate rolls of a die result in 6 each time: The calculator provided considers the case where the probabilities are independent. Calculating the probability is slightly more involved when the events are dependent, and involves an understanding of conditional probability, or the probability of event A given that event B has occurred, P(A|B). Take the example of a bag of 10 marbles, 7 of which are black, and 3 of which are blue. Calculate the probability of drawing a black marble if a blue marble has been withdrawn without replacement (the blue marble is removed from the bag, reducing the total number of marbles in the bag): Probability of drawing a blue marble: P(A) = 3/10 Probability of drawing a black marble: P(B) = 7/10 Probability of drawing a black marble given that a blue marble was drawn: P(B|A) = 7/9 As can be seen, the probability that a black marble is drawn is affected by any previous event where a black or blue marble was drawn without replacement. Thus, if a person wanted to determine the probability of withdrawing a blue and then black marble from the bag: Probability of drawing a blue and then black marble using the probabilities calculated above: P(A ∩ B) = P(A) × P(B|A) = (3/10) × (7/9) = 0.2333 Union of A and BIn probability, the union of events, P(A U B), essentially involves the condition where any or all of the events being considered occur, shown in the Venn diagram below. Note that P(A U B) can also be written as P(A OR B). In this case, the "inclusive OR" is being used. This means that while at least one of the conditions within the union must hold true, all conditions can be simultaneously true. There are two cases for the union of events; the events are either mutually exclusive, or the events are not mutually exclusive. In the case where the events are mutually exclusive, the calculation of the probability is simpler: A basic example of mutually exclusive events would be the rolling of a dice, where event A is the probability that an even number is rolled, and event B is the probability that an odd number is rolled. It is clear in this case that the events are mutually exclusive since a number cannot be both even and odd, so P(A U B) would be 3/6 + 3/6 = 1, since a standard dice only has odd and even numbers. The calculator above computes the other case, where the events A and B are not mutually exclusive. In this case: P(A U B) = P(A) + P(B) - P(A ∩ B) Using the example of rolling dice again, find the probability that an even number or a number that is a multiple of 3 is rolled. Here the set is represented by the 6 values of the dice, written as:
Exclusive OR of A and BAnother possible scenario that the calculator above computes is P(A XOR B), shown in the Venn diagram below. The "Exclusive OR" operation is defined as the event that A or B occurs, but not simultaneously. The equation is as follows: As an example, imagine it is Halloween, and two buckets of candy are set outside the house, one containing Snickers, and the other containing Reese's. Multiple flashing neon signs are placed around the buckets of candy insisting that each trick-or-treater only takes one Snickers OR Reese's but not both! It is unlikely, however, that every child adheres to the flashing neon signs. Given a probability of Reese's being chosen as P(A) = 0.65, or Snickers being chosen with P(B) = 0.349, and a P(unlikely) = 0.001 that a child exercises restraint while considering the detriments of a potential future cavity, calculate the probability that Snickers or Reese's is chosen, but not both: 0.65 + 0.349 - 2 × 0.65 × 0.349 = 0.999 - 0.4537 = 0.5453 Therefore, there is a 54.53% chance that Snickers or Reese's is chosen, but not both. Normal DistributionThe normal distribution or Gaussian distribution is a continuous probability distribution that follows the function of: where μ is the mean and σ2 is the variance. Note that standard deviation is typically denoted as σ. Also, in the special case where μ = 0 and σ = 1, the distribution is referred to as a standard normal distribution. Above, along with the calculator, is a diagram of a typical normal distribution curve. The normal distribution is often used to describe and approximate any variable that tends to cluster around the mean, for example, the heights of male students in a college, the leaf sizes on a tree, the scores of a test, etc. Use the "Normal Distribution" calculator above to determine the probability of an event with a normal distribution lying between two given values (i.e. P in the diagram above); for example, the probability of the height of a male student is between 5 and 6 feet in a college. Finding P as shown in the above diagram involves standardizing the two desired values to a z-score by subtracting the given mean and dividing by the standard deviation, as well as using a Z-table to find probabilities for Z. If, for example, it is desired to find the probability that a student at a university has a height between 60 inches and 72 inches tall given a mean of 68 inches tall with a standard deviation of 4 inches, 60 and 72 inches would be standardized as such: Given μ = 68; σ = 4 The graph above illustrates the area of interest in the normal distribution. In order to determine the probability represented by the shaded area of the graph, use the standard normal Z-table provided at the bottom of the page. Note that there are different types of standard normal Z-tables. The table below provides the probability that a statistic is between 0 and Z, where 0 is the mean in the standard normal distribution. There are also Z-tables that provide the probabilities left or right of Z, both of which can be used to calculate the desired probability by subtracting the relevant values. For this example, to determine the probability of a value between 0 and 2, find 2 in the first column of the table, since this table by definition provides probabilities between the mean (which is 0 in the standard normal distribution) and the number of choices, in this case, 2. Note that since the value in question is 2.0, the table is read by lining up the 2 row with the 0 column, and reading the value therein. If, instead, the value in question were 2.11, the 2.1 row would be matched with the 0.01 column and the value would be 0.48257. Also, note that even though the actual value of interest is -2 on the graph, the table only provides positive values. Since the normal distribution is symmetrical, only the displacement is important, and a displacement of 0 to -2 or 0 to 2 is the same, and will have the same area under the curve. Thus, the probability of a value falling between 0 and 2 is 0.47725 , while a value between 0 and 1 has a probability of 0.34134. Since the desired area is between -2 and 1, the probabilities are added to yield 0.81859, or approximately 81.859%. Returning to the example, this means that there is an 81.859% chance in this case that a male student at the given university has a height between 60 and 72 inches. The calculator also provides a table of confidence intervals for various confidence levels. Refer to the Sample Size Calculator for Proportions for a more detailed explanation of confidence intervals and levels. Briefly, a confidence interval is a way of estimating a population parameter that provides an interval of the parameter rather than a single value. A confidence interval is always qualified by a confidence level, usually expressed as a percentage such as 95%. It is an indicator of the reliability of the estimate. Z Table from Mean (0 to Z)
How do you find the probability between two numbers?The probability that a standard normal random variables lies between two values is also easy to find. The P(a < Z < b) = P(Z < b) - P(Z < a). For example, suppose we want to know the probability that a z-score will be greater than -1.40 and less than -1.20.
How do you find the probability of the mean of a sample?Suppose we draw a sample of size n=16 from this population and want to know how likely we are to see a sample average greater than 22, that is P( > 22)? So the probability that the sample mean will be >22 is the probability that Z is > 1.6 We use the Z table to determine this: P( > 22) = P(Z > 1.6) = 0.0548.
What is the probability that the sample mean will be more than?What is the probability of getting a sample mean greater than the population mean? The probability of getting a sample mean greater than μ (population mean) is 50%, as long as your sampling distribution follows a normal distribution (this occurs if the population distribution is normal or the sample size is large).
How do you solve for the mean of the sampling distribution of sample mean?If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size. For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean μX=μ and standard deviation σX=σ/√n, where n is the sample size.
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Probability of sample mean between two numbers calculator
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