For each of the a) through e) determine whether the sampling distribution of is

Question

For each of the a) through e) determine whether the sampling distribution of is normal, approximately normal, or unknown:

a) The mean amount of sleep that 20- to 24-year-old women get per night is 9.3 hours (Source: Bureau of Labor Statistics). Assume that the population standard deviation
is =1. Samplesofsizen=9aretaken.

b) Prices for boned trout are normally distributed, with = $4.00 per pound and = $0.50. A random sample of size n = 8 is taken.

c) The pollen count distribution for Los Angeles in September is not normally distributed but has a mean = 10 and standard deviation = 2. A random sample of size 60 is taken.

d) The gas mileage for a 2014 Toyota Prius hybrid vehicle is not normally distributed with = 55 miles per gallon and = 8. A random sample of size n = 16 is taken.

e) The gas mileage for a 2014 Toyota Prius hybrid vehicle is not normally distributed with = 55 miles per gallon and = 8. A random sample of size n = 80 is taken.

Explanation / Answer

a)

as sample size is less than 30 and population is not normally distributed ; sampling distribution is unknown

b)

as population is normally distributed therefore sampling distribution is  normally distributed

c)

as sample size is greater than 30 ; sampling distribution is approximately normal

d)

as sample size is less than 30 and population is not normally distributed ; sampling distribution is unknown

e)

as sample size is greater than 30 ; sampling distribution is approximately normal

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