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Complete Question
The amount of money spent on textbooks by a student during a semester at Norwich averages $340.00 with a standard deviation of $40.00. Find the probability that a randomly chosen student will spend a. less than $400 on textbooks in a semester b. between $400 and $460 on textbooks in a semester c. between $260 and $400 on textbooks in a semester
Answer:
a. 0.93319
b. 0.06546
c. 0.91044
Explanation:
We solve using z score
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = $340
σ is the population standard deviation = $40
a. less than $400 on textbooks in a semester
For x = $400
z = 400 - 340/40
z = 1.5
Probability value from Z-Table:
P(x<400) = 0.93319
b. between $400 and $460 on textbooks in a semester
For x = $400
z = 400 - 340/40
z = 1.5
Probability value from Z-Table:
P(x ≤ 400) = P(x = 400)
= 0.93319
For x = $460
z = 460 - 340/40
z = 3
Probability value from Z-Table:
P(x≤ 460) = (x = 460)
= 0.99865
The probability that a randomly chosen student will spend between $400 and $460 on textbooks in a semester is
P(x = $460) - P(x = $400)
= 0.99865 - 0.93319
= 0.06546
c. between $260 and $400 on textbooks in a semester
For x = $260
z = 260 - 340/40
z = -2
Probability value from Z-Table:
P(x≤ 260) = P(x = 260)
= 0.02275
For x = $400
z = 400 - 340/40
z = 1.5
Probability value from Z-Table:
P(x ≤ 400) = P(x = 400)
= 0.93319
The probability that a randomly chosen student will spend between $260and $400 on textbooks in a semester is
P(x = $400) - P(x = $260)
= 0.93319 - 0.02275
= 0.91044