Question

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.4 pounds, what is the probability that the sample mean will be each of the following?

a. More than 59 pounds

b. More than 57 pounds

c. Between 56 and 57 pounds

d. Less than 53 pounds

e. Less than 48 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

Answer 1

X : usage of aluminium of households.

population mean () = 56.8

population sd () = 12.4

The central limit theorem states that for a population with mean μ and standard deviation σ ,if we have sufficiently large random samples from the population(n>30), then the distribution of the sample means will be approximately normally distributed.

here, sample size (n) = 50

so, using the CLT, the distribution for the sample mean be:-

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