Question

The contents of soft drink bottles are normally distributed with a mean of 12 ounces and a standard deviation of 0.2 ounce. Use excel to get answers

(a) what is the probability that a random selected bottle will contain less than 11.5 ounces?

(b) What is the probability that a randomly selected bottle will contain between 11.5 and 12.5 ounces?

(c) What is the probability that a randomly selected bottle will contain more than 12.5 ounces?

(d) What is the probability that a randomly selected bottle will contain exactly 12 ounces?

Answer 1

We are given the distribution as:

a) The probability that a random selected bottle will contain less than 11.5 ounces is computed using the EXCEL function as:

= NORM.DIST(11.5,12,0.2,TRUE)

The required probability here is: 0.0062

b) The probability here is computed as:

= NORM.DIST(12.5,12,0.2,TRUE) - NORM.DIST(11.5,12,0.2,TRUE)

The required probability here is: 0.9876

c) The probability that a randomly selected bottle will contain more than 12.5 ounces is computed here as:

= 1 - NORM.DIST(12.5,12,0.2,TRUE)

The required probability here is: 0.0062

d) As this is a normal distribution, the probability here is computed as:

= NORM.DIST(12 , 12,0.2,FALSE)

The required probability here is: 0.0199