tommy wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. in fact, his times between pitches are normally distributed with a mean of 36 seconds and a standard deviation of 2.5 seconds. what percentage of his times between pitches are a. longer than 39 seconds? b. between 29 and 34 seconds?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell-shaped curve represents the probability.

How to use z-table?

Step 1: In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.9 1.4, 2.2, 0.5, etc.)

Step 2:Then look up at the top of the z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.95 then go for the 0.05 column)

Step 3:Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2. We want to find out the probability that what percentage of his times between pitches are longer than 31 seconds.

Here, In the given question: we have,

Mean=36 seconds

Standard deviation = 2.5 seconds

So,

For x>39

We want to find out the probability that what percentage of his times between pitches are longer than 39 seconds.

[tex]\begin{aligned}&P(X > 39)=1-P(X < 39) \\&P(X > 39)=1-P\left(Z < \frac{x-\mu}{F}\right) \\&P(X > 39)=1-P\left(Z < \frac{39-36}{2.5}\right) \\&P(X > 31)=1-P\left(Z < \frac{3}{2.5}\right) \\&P(X > 39)=1-P(Z < 1.2)\end{aligned}[/tex]

The z-score corresponding to 1.2 is 0.8849

[tex]\begin{aligned}&P(X > 39)=1-0.8849 \\&P(X > 39)=0.1151 \\&P(X > 39)=11.51 \%\end{aligned}[/tex]

Therefore, 11.51% of his times between pitches are longer than 39 seconds.

To learn more about Normal distribution visit:

https://brainly.com/question/4079902

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