Delivery times for shipments from a central warehouse are exponentially distribu

Question

Delivery times for shipments from a central warehouse are exponentially distributed with a mean of 1.84 days (note that times are measured continuously, not just in number of days). The standard deviation of an exponential distribution is equal to the mean of 1.84 days. A random sample of 82 shipments are selected and their shipping times are observed.

Use the Central Limit Theorem to find the probability that the mean shipping time for the 82 shipments is less than 1.48 days.

Round answer to 4 decimal places.

Explanation / Answer

Ans:

Sampling distribution of sample means will follow normal distribution with:

mean=1.84

standard deviation=1.84/sqrt(82)=0.2032

z=(1.48-1.84)/0.2032

z=-1.772

P(z<-1.772)=0.0382

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