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