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Sophie [7]
3 years ago
11

Trucks in a delivery fleet travel a mean of 110 miles per day with a standard deviation of 38 miles per day. The mileage per day

is distributed normally. Find the probability that a truck drives between 132 and 159 miles in a day.
Mathematics
1 answer:
Montano1993 [528]3 years ago
6 0

Answer: 0.1824

Step-by-step explanation:

Given : The mileage per day is distributed normally with

Mean : \mu=110\text{ miles per day}

Standard deviation :  \sigma=38\text{ miles per day}

Let X be the random variable that represents the distance traveled by truck in one day .

Now, calculate the z-score :-

z=\dfrac{x-\mu}{\sigma}

For x= 132 miles per day.

z=\dfrac{132-110}{38}\approx0.58

For x= 159 miles per day.

z=\dfrac{159-110}{38}\approx1.29

Now by using standard normal distribution table, the  probability that a truck drives between 132 and 159 miles in a day will be :-

P(132

Hence, the probability that a truck drives between 132 and 159 miles in a day =0.1824

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