Question

The weight of a product is normally distributed with a standard deviation of 0.5 grams. If the production manager wants no more than 5% of the products to weigh more than 5.1 grams, then the average weight should be _____.

Answer 1

Answer:

4.28 grams

Explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by the formula:

$z=\frac{x-\mu}{\sigma} \\\\where\ \mu=mean,\sigma=standard \ deviation,\ x=raw\ score$

Given that:

P(x > 5.1 grams) = 5%, x = 5.1 grams, σ = 0.5 grams

P(x > 5.1 grams) = 5%

P(x < 5.1 grams) = 100% - 5% = 95%

P(x < 5.1) = 95%

From the normal distribution table, 95% corresponds with a z score of 1.645. Hence:

$1.64=\frac{5.1-\mu}{0.5}\\\\5.1-\mu=0.82\\\\\mu=4.28\ grams$