4.14. A beverage company makes weekly deliveries from its warehouse to a supermarket. The delivery time varies based on interstate traffic and scheduling factors, but is normally distributed with a mean of 17 hours and a standard deviation of 3 hours. What is the probability it will take between 12 and 15 hours to make this weeks delivery?

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4.14. A beverage company makes weekly deliveries from its warehouse to a supermarket. The
delivery time varies based on interstate traffic and scheduling factors, but is normally distributed
with a mean of 17 hours and a standard deviation of 3 hours. What is the probability it will take
between 12 and 15 hours to make this weeks delivery?
Transcribed Image Text:4.14. A beverage company makes weekly deliveries from its warehouse to a supermarket. The delivery time varies based on interstate traffic and scheduling factors, but is normally distributed with a mean of 17 hours and a standard deviation of 3 hours. What is the probability it will take between 12 and 15 hours to make this weeks delivery?
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A normal distribution follows a bell shaped curve which is centred at the mean and it is also called Gaussian distribution. The normal distribution with 0 mean and 1 standard deviation is called standard normal distribution.

The relation between a normal random variable x and z-score is z=x-μσ, where μ is mean and σ is standard deviation  of x. The probability that random variable lies in an interval is equal to the area of that interval.

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