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It is known that amounts of money spent on textbooks in a year by students follow...

It is known that amounts of money spent on textbooks in a year by students follow a normal distribution with mean $380 and standard deviation $50. Find the shortest range of dollar spending on textbooks in a year that includes 60% of all students.

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Answer #1

In this case, we are given

=$380

=$50

We are required to find Zo such that

Refer to standard normal probability distribution tables or some online/offline calculators

(I have used some offline calculator to get the value of z)

z=0.8416 (standard tables given z=0.84)

z=0.8416*50=42.08

Lower amount of money spent=350-42.08=$307.92

Upper amount of money spent=350+42.08=$392.08

Money spent will be between $307.92 and $392.08

Range=392.08-307.92=$84.16

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