Question

Question 6 (1 point) Suppose that one-way commute times in a particular city are normally distributed with a mean of 26.71 minutes and a standard deviation of 2.118 minutes. Would it be unusual for a commute time to be between 24.7 and 25.2 minutes? 0 1) A value in this interval is borderline unusual. 2) A value in this interval is unusual. 3) We do not have enough information to determine if a value in this interval is unusual 4) It is impossible for a value in this interval to occur with this distribution of data. 5) A value in this interval is not unusual

Answer 1

X ~ N ( µ = 26.71 , σ = 2.118 )
P ( 24.7 < X < 25.2 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 24.7 - 26.71 ) / 2.118
Z = -0.95
Z = ( 25.2 - 26.71 ) / 2.118
Z = -0.71
P ( -0.95 < Z < -0.71 )
P ( 24.7 < X < 25.2 ) = P ( Z < -0.71 ) - P ( Z < -0.95 )
P ( 24.7 < X < 25.2 ) = 0.2379 - 0.1713
P ( 24.7 < X < 25.2 ) = 0.0666

5) A value in this interval is not unusual.

Because, the probability 0.0666 is greater than 5% i.e 0.05.