Chapter 13.2, Problem 57E

To determine

To find: The probability that a randomly selected housefly has a wing length of at least 5 millimeters.

Answer to Problem 57E

The probability that a randomly selected housefly has a wing length of at least 5 millimeters is approximately 0.16.

Explanation of Solution

Given:

The wing lengths of houseflies are normally distributed with mean 4.6 millimeters and standard deviation 0.4 millimeter.

Calculation:

From the given data, $\mu =4.6$ and $\sigma =0.4$ .

To find the probability for the given wing length, first, the z statistic for $x=5$ needs to be determined as shown below:

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ =\frac{5-4.6}{0.4}\\ =\frac{0.4}{0.4}\\ =1.0\end{array}$

So, $P\left(x\ge 5\right)=P\left(z\ge 1.0\right)$ . Solve using the standard normal table as shown below:

  $\begin{array}{c}P\left(x\ge 5\right)=P\left(z\ge 1.0\right)\\ =1-P\left(z\le 1.0\right)\left[\because \text{the normal curve is symmetric}\right]\\ \approx 1-0.84\left[\text{From the table}\right]\\ =0.16\end{array}$

So, the probability is approximately 0.16.