Question

The commute time X each working day has the mean of 1 hour and standard deviation of 0.3 hours.

(1) What is the approximate distribution of the average daily commute time for a period of 36 days, by the Central limit theorem? Include the parameters.

(2) Find the probability that the average daily commute time for this period is larger than 1.06 hours.

Answer 1

Solution :

Given that ,

mean = = 1

standard deviation = = 0.3

1)

Approximate distribution is normal .

n = 36

= 1 and

= / n = 0.3 / 36 = 0.3 / 6 = 0.05

2)

P( > 1.06) = 1 - P( < 1.06)

= 1 - P(( - ) / < (1.06 - 1) / 0.05)

= 1 - P(z < 1.2)

= 1 - 0.8849

= 0.1151

Probability = 0.1151