The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ = 382 and a standard deviation of: σ = 21.

According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester?

2.5% of students spent more then 423.16 on textbooks

Step-by-step explanation:

* Lets explain how to solve the problem

- The distribution of the amount of money spent by students on

textbooks in a semester is approximately normal in shape with a

mean of μ = 382 and a standard deviation of σ = 21

- We need to find according to the standard deviation rule, almost 2.5%

of the students spent more than what amount of money on textbooks

in a semester

∵ We have μ, σ, P (x) then to find x we must find the z-score which

corresponding to P (x)

∵ P (x) = 2.5% = 2.5/100 = 0.025

∵ P (x >?) = 1 - P (z >?)

∴ 0.025 = 1 - P (z >?)

∴ P (z >?) = 1 - 0.025 = 0.975

- Lets find the corresponding value for the area of 0.975 from the

normal distribution table

∴ The value of z corresponding to 0.975 = 1.96

∵ x = μ + zσ

∵ μ = 382 and σ = 21

∴ x = 382 + 1.96 * 21 = 382 + 41.16 = 423.16

∴ The amount of money is 423.16

∴ 2.5% of students spent more then 423.16 on textbooks