Question

the number of days (x) after mailout it takes a utility company to receive payment for a customers bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days. about 16% of bills will be received earlier than -- days after mailout. question 6 according to the bureau of labor statistics, in may 2014 the mean hourly wage of a social worker was $28.08 with a standard deviation of $1.97. jeronica is a social worker with an

Explanation:

Step1: Recall the properties of the standard normal distribution

We know that for a normal distribution $X\sim N(\mu,\sigma^{2})$, we use the $z -$score formula $z=\frac{x-\mu}{\sigma}$, and we want to find the $x$ value such that $P(X < x)=0.16$. Looking up the $z -$score in the standard - normal distribution table (the $z$ value corresponding to a left - tail probability of $0.16$), we find that $z\approx - 1$.

Step2: Rearrange the $z -$score formula to solve for $x$

Given $z=\frac{x-\mu}{\sigma}$, we can rewrite it as $x=\mu + z\sigma$. We are given that $\mu = 31$ and $\sigma = 6$, and $z=-1$.
Substitute the values into the formula: $x=31+( - 1)\times6$.

Step3: Calculate the value of $x$

$x=31 - 6=25$.

Answer:

25