Question

(3 pts) For students in a certain region, scores of students on a standardized test approximately follow a normal distribution with mean μ=543.4 and standard deviation σ=30. In completing the parts below, you should use the normal curve area table that is included in your formula packet.

(a) What is the probability that a single randomly selected student from among all those in region who took the exam will have a score of 548 or higher?
ANSWER:  

For parts (b) through (e), consider a random sample of 30 students who took the test.

(b) The mean of the sampling distribution of x¯ is

(c) The standard deviation of the sampling distribution of x¯ is

(d) What z-score corresponds to the mean score of x¯ = 548?
ANSWER:

(e) What is the probability that the mean score x¯ of these 30 students will be 548 or higher?
ANSWER:  

Answer 1

(a). It is given that

The z-score formula is given by,

(b). The mean of the sample distribution is the same as the population mean (mu)

c). Standard deviation of sampling distribution is given by the following formula,

Where n = 30

d). The formula for z-score for sampling distribution is given by

(e). We already calculated z-score in part d. Looking up the p-value for z=0.84, we find