(1 point) The scores of students on the SAT college entrance examinations at a
certain high school had a normal distribution with mean μ = 546.2 and standard
deviation σ = 26.9.
(a) What is the probability that a single student randomly chosen from all those taking
the test scores 552 or higher?
ANSWER:
For parts (b) through (d), consider a simple random sample (SRS) of 30 students who
took the test.
(b) What are the mean and standard deviation of the sample mean score, of 30
students?
The mean of the sampling distribution for is:
The standard deviation of the sampling distribution for is:
(c) What z-score corresponds to the mean score of 552?
ANSWER:
(d) What is the probability that the mean score of these students is 552 or higher?
ANSWER:
(1 point)
Enter any probabilities as decimals (not percentages). Use at least five significant
digits.
Spiders will occasionally hitchhike from the tropics to the US in shipments of fruit,
including bananas. The number of spiders in a shipment of bananas varies from
shipment to shipment, but has a mean of 6.3 and a standard deviation of 1.2. An
importer randomly samples 28 shipments for inspection and calculates a sample
mean number of spiders per shipment. We know there is a particular kind of
distribution that can be used to approximate a sample mean. Use that approximation
for the rest of this problem.
(a) What is the mean of the sample mean number of spiders?
(b) What is the standard deviation of the sample mean number of spiders?
(c) What is the probability the sample mean number of spiders is less than 6.78?
(d) What is the value such that the sample mean has probability 0.6 of being greater?