Question

Tommy Wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. In fact, his time between pitches are normally distributed with a mean of seconds and a standard deviation of seconds. What percentage of his times between pitches are longer than seconds

Answer 1

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Tommy Wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. In fact, his time between pitches are normally distributed with a mean of 29 seconds and a standard deviation of 2.1 seconds. What percentage of his times between pitches are longer than 31 seconds ?

Given Information:  

Mean pitching time = μ = 29 seconds

Standard deviation of pitching time = σ = 2.1 seconds

Required Information:  

P(X > 31) = ?

Answer:

$P(X > 31) = 17.11 \%$

Step-by-step explanation:

What is Normal Distribution?

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.  

We want to find out the probability that what percentage of his times between pitches are longer than 31 seconds.

$P(X > 31) = 1 - P(X < 31)\\P(X > 31) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\P(X > 31) = 1 - P(Z < \frac{31 - 29}{2.1} )\\P(X > 31) = 1 - P(Z < \frac{2}{2.1} )\\P(X > 31) = 1 - P(Z < 0.95)$

The z-score corresponding to 0.95 is 0.8289

$P(X > 31) = 1 - 0.8289\\P(X > 31) = 0.1711\\P(X > 31) = 17.11 \%$

Therefore, 17.11% of his times between pitches are longer than 31 seconds.

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 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 0.05 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.