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Assume that the sample is taken from a large
Chapter 6, Problem 21E(choose chapter or problem)
Problem 21E
Assume that the sample is taken from a large population and the eorrection factor can be ignored.
Annual PrecipitationThe average annual precipitation for a large Midwest city is 30.85 inches with a standard deviation of 3.6 inches. Assume the variable is normally distributed.
a. Find the probability that a randomly selected month will have less than 30 inches.
b. Find the probability that the mean of a random selection of 32 months will have a mean less than 30 inches.
c. Does it seem reasonable that one month could have a rainfall amount less than 30 inches?
d. Does it seem reasonable that the mean of a sample of 32 months could be less than 30 inches?
Questions & Answers
QUESTION:
Problem 21E
Assume that the sample is taken from a large population and the eorrection factor can be ignored.
Annual PrecipitationThe average annual precipitation for a large Midwest city is 30.85 inches with a standard deviation of 3.6 inches. Assume the variable is normally distributed.
a. Find the probability that a randomly selected month will have less than 30 inches.
b. Find the probability that the mean of a random selection of 32 months will have a mean less than 30 inches.
c. Does it seem reasonable that one month could have a rainfall amount less than 30 inches?
d. Does it seem reasonable that the mean of a sample of 32 months could be less than 30 inches?
ANSWER:
Solution :
Step 1 of 4:
Given the mean inches, the standard deviation
3.6 inches.
a). We need to find the probability that less than 30 inches.
The z-score is the sample mean decreased by the mean divided by the standard deviation.
z =
z =
z =
z = -0.23611
Hence, z-score is -0.24.
Now we have to determine the probability.
Using area under the normal curve table,
P(X<30) = P(z<-0.23)
P(X<30) = 0.4090
Therefore, the probability that less than 30 inches is 0.4090.