Question

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce.

Give the answers correct to four decimals.

a) What is the probability the contents of a single cup will be greater than 12.1 ounces?


b) If a sample of 9 cups is selected, what is the probability that the mean of the sample will be greater than 12.1 ounces?

Answer 1

a) The probability is 0.308538.

b) The probability is 0.066807.

What is probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

mean= 12 ounce

standard deviation = 0.2 ounce

a) The  probability the contents of a single cup will be greater than 12.1 ounces

P( x> 12.1 ounce) = P( x $- \mu_x/ \sigma_x$ > (12.1- 12)/ 0.2)

                           = P( z< 0.1/ 0.2)

                           = P( z< 0.5)

                           = 0.308538

b) If a sample of 9 cups is selected

then, P( x> 12.1) =  P( x $- \mu_x/( \sigma_x/ \sqrt{n} )$ > (12.1- 12)/ (0.2/ √9))

                          = 0.066807

Learn more about probability here:

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