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

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

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step-by-step explanation: