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

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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

a. 0.93319

b. 0.06546

c. 0.91044

Step-by-step 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

c

step-by-step explanation: