Question

Suppose that newborn harbor seal pups have a weight that is normally distributed, with a mean of 22.0 lbs and standard deviation of 1.1 lbs. Find the probability that a newborn pup has a weight above 24.0 lbs.

Answer 1

0.0344 = 3.44% probability that a newborn pup has a weight above 24.0 lbs.

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 22.0 lbs and standard deviation of 1.1 lbs.

This means that
`\mu = 22, \sigma = 1.1`

Find the probability that a newborn pup has a weight above 24.0 lbs.

This is 1 subtracted by the p-value of Z when X = 24. So

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

`Z = (24 - 22)/(1.1)`

`Z = 1.82`

`Z = 1.82` has a p-value of 0.9656.

1 - 0.9656 = 0.0344

0.0344 = 3.44% probability that a newborn pup has a weight above 24.0 lbs.