Question: This assessment will need to be completed in one sitting and will contain material from Chapter 5…

This assessment will need to be completed in one sitting and will contain material from Chapter 5.

You are to use the Standard normal table from the textbook (also linked in “course resources” module). You will show your work, and there will be a place to upload your work.

I would plan for about an hour for this assessment, although depending on your comprehension of the material it could take less or more time.

1 Numeric 2 points

Under current rules, the weight of a MLB baseball weighs between 142 and 149 grams. One particular company which makes baseballs produces baseballs approximately normally distributed, with mean of 145 grams and standard deviation of 1.38 grams.

What is the probability that a ball chosen at random from this company would be too light (i.e. less than 142 grams) according to MLB standards?

Draw a picture that represents the problem. Show your work.

Type your answer…

2 Numeric 2 points

Under current rules, the weight of a MLB baseball weighs between 142 and 149 grams. One particular company which makes baseballs produces baseballs

Solution

Under current rules, the weight of a MLB baseball is normally distributed with a mean of 145 grams and a standard deviation of 1.38 grams. We need to find the probability that a baseball is too light (i.e., less than 142 grams). First, we convert 142 grams to a standard normal variable (Z-score) using the formula: \[ Z = \frac{X - \mu}{\sigma} \] where \(X\) is the value (142 grams), \(\mu\) is the mean (145 grams), and \(\sigma\) is the standard deviation (1.38 grams). Substitute the values: \[ Z = \frac{142 - 145}{1.38} \] Calculate the Z-score: \[ Z = \frac{-3}{1.38} \approx -2.17 \] Now, we look up the Z-score of \(-2.17\) in the standard normal distribution table or use a calculator to find the probability. The probability corresponding to \(Z = -2.17\) is approximately 0.0150. Thus, the probability that a randomly chosen baseball is too light (weighs less than 142 grams) is 0.0150, or 1.50%.