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 а bout:

Step-by-step 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