A certain city the Transportation Authority (CTA) has trollies leaving regularly

Question

A certain city the Transportation Authority (CTA) has trollies leaving regularly throughout the day beginning at 5:00 a.m. Although the length of a trip and the number of stops are constant, the time taken for each trip varies due to weather, traffic, and time of the day. According to the CTA, the mean time taken for the trip is 50 minutes. Suppose the travel time is Normally distributed with standard deviation 4 minutes. A random sample of 25 trips is obtained, and the time for each 1s recorded (a) Find the probability that the sample mean time will be less than 48 minutes. (b) Find the probability that the sample mean time will be within one minute of the population mean (50 minutes)

Explanation / Answer

a)

b)

for normal distribution z score =(X-)/ here mean=       = 50 std deviation   == 4.0000 sample size       =n= 25 std error=x=/n= 0.8000

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