Chapter 7, Problem 7.1TI

An unknown distribution has a mean of 45 and a standard deviation of eight. Samples of size n = 30 are drawn randomly from the population. Find the probability that the sample mean is between 42 and 50.

To determine

To calculate:

The probability that the sample mean is between $42$ and $50$.

Answer to Problem 7.1TI

$P\left(42<\overline{X}<50\right)=0.9797$.

Explanation of Solution

Given information:

Mean = $45$

Standard deviation = $8$

$n=30$

Formula used:

$\overline{X}\sim N\left({\mu }_x,\frac{\sigma x}{\sqrt{n}}\right)$

Calculation:

$\begin{array}{l}\overline{X}\sim N\left(45,\frac{8}{\sqrt{30}}\right)\\ P\left(42<\overline{X}<50\right)=normalcdf\left(42,50,45,\frac{8}{\sqrt{30}}\right)\\ P\left(42<\overline{X}<50\right)=0.9797\end{array}$.