Question

a fruit package company produced peaches last summer whose weights were normally distributed with the mean 14 ounces and standard deviation 0.4 ounce. among a sample of 1000 of those peaches about how many could be expected to have any weights of more than 12.6 ounces?round to the nearest whole number as needed

Answer 1

Let x be the random representing the weights of the peaches produced by the company. Since the weights are normally distributed and the population mean and standard deviation are known, we would apply the formula,

z = (x - mean)/standard deviation

From the information given,

mean = 14

standard deviation = 0.4

For the weights to be more than 12.6 ounce, the equation would be

`z\text{ = }\frac{(12.6\text{ - 14)}}{0.4}`

z = -3.5

Looking at the normal distribution table, the probability corresponding to the z score of - 3.5 is 0.00023

Since we want to determine propability for the weights greater than 12.6 ounce, the required probability would be

1 - 0.00023 = 0.99977

Given that the total number of peaches is 1000, the number of peaches expected to have weights more than 12.6 ounce is

0.99977 * 1000 = 999.77

Rounding to the nearest whole number, it becomes 1000

The number of peaches expected to have weights more than 12.6 ounce is approximately 1000