The amount of money spent per person at a state fair is distributed normally, with a mean of $32 and a standard deviation of $3.75.

If 1200 people attend the fair, how many people would you expect to spend between 24.50 and 35.75?

Mean: $32

Standard Deviation: $3.75

Answer: 737 people are expected to spend between 24.50 and 35.75

Step-by-step explanation:

Since the amount of money spent per person at a state fair is distributed normally, we would apply the formula for normal distribution.

z = (x - u) / s

Where

u = mean

s = standard deviation

x = number of people that spent a certain amount of money.

From the information given

u = 32

s = 3.75

We want to find

P (24.5 lesser than or equal to x lesser than or equal to 35.75)

For x = 24.5,

z = (24.5 - 32) / 3.75 = - 7.5/3.75

z = - 2

Looking at the normal distribution table, the corresponding z score is 0.2275

For x = 35.75,

z = (35.75 - 32) / 3.75 = 3.75/3.75

z = 1

Looking at the normal distribution table, the corresponding z score is 0.8413

P (24.5 lesser than or equal to x lesser than or equal to 35.75)

= 0.8413 - 0.2275 = 0.6138

The number of expected people will be

0.6138 * 1200 = 737