Question

The weights of ice cream cartons are normally distributed with a mean weight of 12 ounces and a standard deviation of 0.4 ounce.(a) What is the probability that a randomly selected carton has a weight greater than 12.14 ounces?(b) A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 12.14 ounces?

Answer 1

The weights of ice cream cartons are normally distributed with a mean weight of 12 ounces and a standard deviation of 0.4 ounce.

(a) What is the probability that a randomly selected carton has a weight greater than 12.14 ounces?

(b) A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 12.14 ounces?

Part a

Remember that

z =(x - μ)/σ

we have

μ=12 oz

σ=0.4 oz

x=12.14

Fond out the z-score

z=(12.14-12)/0.4

z=0.35

using a z-score tables

we have

P=0.36317

the answer part a is P=0.36317

Part b

A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 12.14 ounces?

the formula is equal to

`\begin{gathered} \\ z=\frac{(x-\mu)}{\frac{\sigma}{\sqrt[]{n}}} \end{gathered}`

we have

μ=12 oz

σ=0.4 oz

x=12.14

n=25

substitute

`\begin{gathered} z=\frac{(12.14-12)}{\frac{0.4}{\sqrt[]{25}}} \\ z=1.75 \end{gathered}`

using z-scores tables

P=0.04