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Blababa [14]
2 years ago
7

A mile-runner’s times for the mile are normally distributed with a mean of 4 min. 3 sec. (This would have to be expressed in dec

imal minutes -- 4.05 minutes), and a standard deviation of 2 seconds (0.0333333··· minutes (the three dots indicate a repeating decimal)). What is the probability that on a given run, the time will be 4 minutes or less?
Mathematics
1 answer:
Vinvika [58]2 years ago
8 0

Answer: 0.0668

Step-by-step explanation:

Given: Mean : \mu=\text{4 min. 3 sec.=4.05 minutes}

Standard deviation : \sigma = \text{2 seconds=0.033333 minutes }

The formula to calculate z-score is given by :_

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

For x= 4 minutes  , we have

z=\dfrac{4-4.05}{0.03333}\approx-1.5

The P-value = P(z\leq-1.5)=0.0668072\approx0.0668

Hence, the probability that on a given run, the time will be 4 minutes or less = 0.0668

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