The median age of residents of the United States is 31 years. If a survey of 100 randomly selected U. S. residents is to be taken, use the normal approximation to the binomial distribution to approximate the probability that at least 57 will be under 31 years of age.

P (x≥ 57) = 6.7789 e^-8

Step-by-step explanation:

Here n= 100

p = 31/100 = 0.31

We formulate the null hypothesis that H0: p= 0.31 against the claim Ha: p≠0.31

The significance level is chosen to be ∝= 0.05

The test statistic x to be used is X, the number  U.S. residents is to be taken which is at least 57

The binomial calculator gives the

P (x≥ 57) = 6.7789 e^-8

IF ∝= 0.05 then ∝/2 = 0.025

We observe that P (x≥ 57) is less than 0.025

Hence we reject H0 and conclude that p ≠0.31

This is true because for normal distribution the median = mean which is usually the 50 % of the data.