Chapter 12.7, Problem 6CYU

To determine

To Find: The probability that no more than 350 of the surveyed upperclassmen have the summer jobs.

Answer to Problem 6CYU

The required probability is $0.0239$ .

Explanation of Solution

Given:

The $x$ is the random variable show the number of upperclassmen have the summer jobs and x has the binomial distribution with the parameters of $n=6$ and $s=0.85$ .

Calculation:

From the given data the normal distribution of the mean is obtained as,

  $\begin{array}{c}\mu =ns\\ =200\cdot 0.85\\ =170\end{array}$

The standard deviation is,

  $\begin{array}{c}\sigma =\sqrt{nsf}\\ =\sqrt{200\cdot 0.85\cdot 0.15}\\ =5.05\end{array}$

The z score of the $x=160$ is,

  $\begin{array}{c}z=\frac{x-u}{\sigma }\\ =\frac{160-170}{5.05}\\ -1.98\end{array}$

Then, the probability that no more than 160 of the surveyed upperclassmen have summer jobs is,

  $\begin{array}{c}P\left(x\le 160\right)=P\left(z\le -1.98\right)\\ =0.0239\end{array}$