Question

to be graded extra large an egg must weight at least 2.2 ounces. if the average weight for an egg is 1.7 ounces with a standard deviation of 0.4. how many of seven dozen randomly chosen eggs would you expect to be extra large? round to the nearest whole number as needed

Answer 1

Let x be a random variable representing the weight of a selected egg. Let us assume that the selected eggs are normally distributed. Since we know the population mean and standard deviation, we would determine the z score by applying the formula,

z = (x - mean)/standard deviation

For an egg to be graded as extra large, it's weight must be at least 2.2 ounces. The probability of selecting an eggs that weighs at least 2.2 ounces is expressed as

`\begin{gathered} P(x\text{ }\ge2.2) \\ It\text{ can also be written as} \\ 1\text{ - P(x < 2.2)} \end{gathered}`

Given that

mean = 1.7

standard deviation = 0.4

x = 2.2

z = (2.2 - 1.7)/0.4 = 1.25

Looking at the normal distribution table, the probability value corresponding to a z score of 1.25 is 0.8944

`\begin{gathered} P(x\text{ < 2.2) = 0.8944} \\ P(x\text{ }\ge2.2)\text{ = 1 - 0.8944 = 0.1056} \end{gathered}`

Given that the total number of eggs is seven dozens,

7 dozens = 7 * 12 = 84

The expected number of extra large eggs that is expected to be selected from 84 eggs is

0.1056 * 84 = 8.8704

Rounding to the nearest whole number, it becomes 9 eggs