Question

The amount of money spent on books by Hunter students in a semester is normally distributed with a mean μ = $249, standard deviation σ = $30.

What is the probability that a randomly chosen student from this populaiton will have spent between $200 and $300.

(Use the z table or Excel to calculate and enter a probability .00 to 1.00)

Answer 1

Here, μ = 249, σ = 30, x1 = 200 and x2 = 300. We need to compute P(200<= X <= 300). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (200 - 249)/30 = -1.63
z2 = (300 - 249)/30 = 1.7

Therefore, we get
P(200 <= X <= 300) = P((300 - 249)/30) <= z <= (300 - 249)/30)
= P(-1.63 <= z <= 1.7) = P(z <= 1.7) - P(z <= -1.63)
= 0.9554 - 0.0516
= 0.9038

For P(z <= 1.7) value is calculated from table as:

P(z <= -1.63) z value is calculated from table as: