Answer:
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
