Question

Evaluating probability: A particular type of mouse's weights are normally distributed, with a mean of 726 grams and a standard deviation of 23 grams. If you pick one mouse at random, find the following: (round all probabilities to four decimal places) a) What is the probability that the mouse weighs less than 722 grams

Answer 1

0.4325 = 43.25% probability that the mouse weighs less than 722 grams

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 726 grams and a standard deviation of 23 grams.

This means that
`\mu = 726, \sigma = 23`

a) What is the probability that the mouse weighs less than 722 grams

This is the p-value of Z when X = 722. So

`Z = (X - \mu)/(\sigma)`

`Z = (722 - 726)/(23)`

`Z = -0.17`

`Z = -0.17` has a p-value of 0.4325

0.4325 = 43.25% probability that the mouse weighs less than 722 grams