Acompany produces packets of soap
powder that are labeled "giant size 32 ounces." the
actual weight of soap powder in a box has a normal
distribution with a mean of 33 oz. and a standard
deviation of 0.7 oz. 95% of packets actually contain
more than x oz. of soap powder. what is x?
(a) 31.60
(b) 31.85
(c) 32.88
(d) 34.15
(e) 34.40

z-scores illustrates how far a data element is, from the mean of the dataset.

The value of x is (e) 34.40

The given parameters are:

--- mean

--- standard deviation

--- confidence level

First, we determine the z-score from the confidence interval

From the z score table, the corresponding z score of is:

The value of x, is calculated using:

Substitute values for z, and

Multiply both sides by 0.7

Collect like terms

Approximate

Hence, the value of x is (e) 34.40

Read more about z-scores at:

link

(b) 31.85

Explanation:

First, we need to know the z-score for a one-sided confidence interval with 95% coverage. Looking at a z-score table, this value is 1.645. Then: