SOLUTION: The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The standard deviation is 8 minutes. Assume the variable is normally distributed

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Question 1131269: The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The standard deviation is 8 minutes. Assume the variable is normally distributed. Find the probability that a randomly selected adult will complete the test in less than 43 minutes.
Find the probability that if 50 randomly selected adults take the test, the mean time it takes the group to complete the test will be less than 43 minutes.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
for the individual:

z = (x - m) / s

z is the z-score
x is the raw score to be compared against the mean.
m is the mean.
s is the standard deviation.

formula becomes z = (43 - 46.2) / 8 = -.4

area to the left of this z-score = .3445783029.

that's the probability that the randomly selected individual will complete the achievement test in less than 43 minutes.

for the group of 50 individuals:

z = (x - m) / s

z is the z-score
x is the raw score to be compared against the mean.
m is the mean.
s is the standard error

the standard error is the standard deviation of the distribution of sample means.

the formula for standard error is s = standard deviation / sqrt(sample size).

that formula becomes s = 8 / sqrt(50) = 1.3137085

z-score formula becomes z = (43 - 46.2) / 1.3137085 = -2.828427125

area to the left of this z-score = .0023389301

that's the probability that the mean of the randomly selected group of 50 individuals will complete the achievement test in less than 43 minutes.

you are not now looking at the score of one individual.

you are looking at the average score of a group of 50 individuals.

the likelihood that a randomly selected individual will complete the test in less than 43 minutes is much more likely than the likelihood that the average of 50 individuals will complete the test in less than 43 minutes.