Question

Suppose you are interested in measuring the amount of time, on average, it takes you to make your commute to school. You've estimated that the average time is 35.68 minutes with a standard deviation of 6.17 minutes. Assuming that your estimated parameters are correct and the commute time is normally distributed, what is the probability that the average commute time of 11 random days is greater than 36.86 minutes? Question 8 options: 1) 0.2629 2) 0.7371 3) 0.5758 4) 0.8246 5) 0.4242

Answer 1

Solution :

Given that,

mean = = 35.68

standard deviation = = 6.17

n=11

= =35.68

= / n = 6.17 / 11 = 1.8603

P( > 36.86) = 1 - P( <36.86 )

= 1 - P[( - ) / < (36.86-35.68) /1.8603 ]

= 1 - P(z < 0.63)

Using z table

= 1 - 0.736

= 0.2629

probability= 0.2629 approximately