Question

11. The number of gallons of carbonated soft drink consumed per person annually is normally distributed with mean 47.5 and standard deviation 3.5. Twenty-five people are selected at random. The probability that the average number of gallons of carbonated soft drink they each consume per year is between 45 and 50 gallons is about:

Answer 1

Explanation:

Since the number of gallons of carbonated soft drink consumed per person annually is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = number of gallons of carbonated soft drink.

µ = mean

σ = standard deviation

From the information given,

µ = 47.5

σ = 3.5

We want to find the probability that the average number of gallons of carbonated soft drink they each consume per year is between 45 and 50 gallons. It is expressed as

P(45 x ≤ x ≤ 50)

For x = 45,

z = (45 - 47.5)/3.5 = - 0.71

Looking at the normal distribution table, the probability corresponding to the z score is 0.2389

For x = 50,

z = (50 - 47.5)/3.5 = 0.71

Looking at the normal distribution table, the probability corresponding to the z score is 0.758

Therefore,

P(45 x ≤ x ≤ 50) = 0.758 - 0.2389

= 0.5191