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.
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