ounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of 25 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for​ (a) less than 22 minutes, (b) between 25 and 32 minutes, and​ (c) m

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The amounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of 25 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for​ (a) less than 22 minutes, (b) between 25 and 32 minutes, and​ (c) more than40 minutes.

Expert Solution
Step 1

(a)

Given:

μ=25, σ=7

The corresponding z-value needed to be computed:

Statistics homework question answer, step 1, image 1

 The probability that a randomly selected athlete uses a stairclimber for​ less than 22 minutes is,

Statistics homework question answer, step 1, image 2

By using the standard normal table,

Statistics homework question answer, step 1, image 3

Hence, the required probability is 0.3341.

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