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

maya’s expression will generate the wrong sum because she violated the commutative property.

step-by-step explanation:

cause it equals more