Suppose 58% of the population has a retirement account. If a random sample of size 570 is selected, what is the probability that the proportion of persons with a retirement account will be less than 57%

The probability that the proportion of persons with a retirement account will be less than 57%=31.561%

Step-by-step explanation:

We are given that

n=570

p=58%=0.58

We have to find the probability that the proportion of persons with a retirement account will be less than 57%.

q=1-p=1-0.58=0.42

By takin normal approximation to binomial  then sampling distribution of sample proportion  follow normal distribution.

Therefore,

Now,

=31.561%

Hence,  the probability that the proportion of persons with a retirement account will be less than 57%=31.561%

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