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 6 minutes to select a shoe purchase. Is this outcome unusual?

Answer 1

Correct answer is: P(x<6) is 0.123 and it is usual.

Solution:-

Given that the time a person takes to decide which shoes to purchase follows normal distribution. Which has mean = 8.21 minutes and standard deviation 1.90

Then probability of individual takes less than 6 minutes is

P(X<6) = $P(z<\frac{x-mean}{standard deviation} )$

           = $P(z<\frac{6-8.21}{1.90} )=P(z<-1.163)$

           = 0.1230

Typically we say an event with a probability less than 5% is unusual.

But here P(X<6) = 0.123 is greater than 5% hence this is usual.