The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase. is this outcome unusual?

The answer is 0.0918, it is not unusual.

Step-by-step explanation:

Given :

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes

The standard deviation is 1.91  

i.e. minutes and minutes.

Let   denotes the length of time a person takes to decide which shoes to purchase.

Formula :

Then, the probability that a randomly selected individual

It will takes as less than 6 minutes to select a shoe purchase will be the -value

Then

By using -value ]

Thus, the required probability

Since, P-value , it means this outcome is not unusual.

[Note : When a outcome is unusual then the probability of its happening is less than or equal to ]

For more reference about probability,

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).