Question

a) can you tell the speed of craig’s fastest pitch? explain. b) between what speeds does craig usually pitch? c) based on this data, what is the probability that craig will pitch the ball between 70 and 75 miles per hour?

Explanation:

Part (a)

To determine the fastest pitch, we need the maximum value on the horizontal axis (speed) with non - zero frequency. But the histogram's last bar ends at 75 mph, but we don't know if there are pitches at 75 mph or beyond (since the bar for 70 - 75 has a frequency, but we don't know the exact upper limit of the fastest pitch from this histogram alone. The histogram groups speeds into intervals, so we can't tell the exact fastest pitch, only the interval it might be in (up to 75 mph, but maybe less if the last interval has no pitches at the upper end).

To find the usual pitching speeds, we look at the intervals with the highest frequencies. The tallest bar (highest frequency) is around 50 - 55 mph, and other relatively high - frequency bars are around 50 - 65 mph. So the most frequent (usual) speeds are in the interval with the highest frequency, which is 50 - 55 mph, and also considering adjacent high - frequency intervals, the usual speeds are between 50 and 65 mph (since the frequencies are relatively high in 50 - 55, 55 - 60, 60 - 65 intervals).

Step 1: Calculate total number of pitches

First, we sum up the frequencies of all the intervals. The frequencies are: for 45 - 50: 1, 50 - 55: 5, 55 - 60: 3, 60 - 65: 4, 65 - 70: 1, 70 - 75: 2.
Total number of pitches $n=1 + 5+3 + 4+1 + 2=\sum_{i = 1}^{6}f_i=16$.

Step 2: Find frequency of pitches between 70 - 75 mph

The frequency of pitches in the 70 - 75 mph interval is $f = 2$.

Step 3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the favorable outcomes are the number of pitches between 70 - 75 mph, and the total outcomes are the total number of pitches.
So $P=\frac{2}{16}=\frac{1}{8}=0.125$.

Answer:

No, we cannot tell the exact speed of Craig’s fastest pitch. The histogram shows speed intervals (e.g., 45 - 50, 50 - 55, etc.). We know the fastest pitch is in the highest interval shown (up to 75 mph), but we don't have the exact value since the data is grouped into intervals.

Part (b)