The Amazing Race is a reality show where contestants race around the world compl

Question

The Amazing Race is a reality show where contestants race around the world completing various tasks in a variety of locales. Crucial to the show is estimating how long it'll take contestants to complete these tasks. Suppose time-to-completion follows a normal distribution with an average of 55 minutes and standard deviation of 4 minutes. What percent of contestants will take exactly 60 minutes to complete the task?

Express your answer as a percent to one decimal place. Exclude the percent sign (%) in your answer.

Explanation / Answer

Normal distribution

average = 55 mins

sd = 4 mins

percntage of people taking exactly 60 mins =

Lets first find the probability of people taking more and less than 60 mins

P(X>60) = z = 60 - 55 / 4 = 1.25 = 10.565 %(mapping z from the z table)

P(X<60) = 100 - 10.565 = 89.435%

P(X>61) = 6.6807

P(X<59) = 84.1345

Therefore P(59 < X < 61) = 100 - 84.1345 - 6.6807 = 9.1848

P(X = 60) = 0

As area under the curve of the normal distribution comes 0 for the straight line at P(X = 60)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.