Statistical Abstracts (117th edition) provides information aboutthe number of

registered automobiles, including taxis, by state. The number ofregistered
automobiles per 1,000 residents follows an approximately normaldistribution with
mean ì = 514.6 and standard deviation ó = 84.6. In thequestions below, x = number
of registered automobiles per 1,000 residents.
(a) Find the probability that for a random sample of 4 states thesample mean, x is
between 475 and 525.
(b) Find the probability that for a random sample of 16 states thesample mean, x ,
is between 475 and 525.

1 answer

Use a z-table and z-scores. You will have to account for the sample size, so here is the formula:

z = (x - mean)/(sd/√n)

For a): calculate two z-scores
z = (475 - 514.6)/(84.6/√4)
z = (525 - 514.6)/(84.6/√4)

Once you have the two z-scores, find the probability between the two using a z-table.

For b): calculate two z-scores using the same data as a), with the exception of 16 for the sample size.

Find the probability between the two z-scores using a z-table.

I hope this will help get you started.