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Marianna [84]
3 years ago
11

John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a s

tandard deviation of 5.1 minutes. What is the probability that the commute time for a randomly selected day will be between 28 and 34 minutes?
Mathematics
1 answer:
STatiana [176]3 years ago
6 0

Answer:

0.32493

Step-by-step explanation:

We have been given that John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes.

We are asked to find the probability that the commute time for a randomly selected day will be between 28 and 34 minutes.

First of all, we will find z-score corresponding to 28 minutes and 34 minutes. Then, we will find area under normal curve between both z-scores.

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

z=\frac{28-26.7}{5.1}=\frac{1.3}{5.1}=0.25

z=\frac{34-26.7}{5.1}=\frac{7.3}{5.1}=1.43

Now, we need to find the probability between z-score of 1.43 and 0.25.

P(0.25.

Using formula P(a, we will get:

P(0.25

P(0.25

P(0.25

Therefore, the probability, that the commute time for a randomly selected day will be between 28 and 34 minutes, is 0.32493.

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