Question

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase. Is this outcome unusual?Probability is 0.045, which is usual as it is not less than 5%Probability is 0.954, which is unusual as it is greater than 5%Probability is 0.954, which is usual as it is greater than 5%Probability is 0.045, which is unusual as it is less than 5%

Answer 1

Given:

$\begin{gathered} mean(\mu)=8.21 \\ standard-deviation(\sigma)=1.90 \end{gathered}$

To Determine: The probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase

Solution

P(x<5)

The z score formula is given as

$z=\frac{x-\mu}{\sigma}$

Substitute the given into the formula

$z=\frac{5-8.21}{1.90}$$\begin{gathered} z=-\frac{3.21}{1.9} \\ z=-1.68947 \end{gathered}$

The probabilty would be

$\begin{gathered} P(x<-1.68947)=0.04556 \\ \approx0.045 \\ \approx4.5\% \end{gathered}$

Hence, the probability is 0.045, which is unusual as it is less than 5%