Question

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 900 grams?

Answer 1

??

Explanation:

Answer 2

2.28% probability that it will weigh less than 900 grams

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 910, \sigma = 5`

What is the probability that it will weigh less than 900 grams?

This probability is the pvalue of Z when X = 900. So

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

`Z = (900 - 910)/(5)`

`Z = -2`

`Z = -2` has a pvalue of 0.0228.

2.28% probability that it will weigh less than 900 grams