Question

1.) The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean 42 and standard deviation 8. Find the percentile corresponding to p = 36% of the tire lifetimes.

Write only a number as your answer. Round to 2 decimal places.

2.) Electricity bills in a certain city have mean $98.09. Assume bills are normally distributed with standard deviation $17.94. Find the value that seperates the lower 40% of the bills from the rest.

Write only a number as your answer. Round to 2 decimal places.

3.) A survey among freshmen at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 40 and standard deviation 4. Find percentile corresponding to p = 38% of the number of hours studying.

Write only a number as your answer. Round to 2 decimal places.

Answer 1

.1)

Here and

Here we need to find x such that

Now using z table we get

So

#Find the percentile corresponding to p = 36% of the tire lifetimes. is 39.13

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2)Find the z-value that has a 40 % left tail.
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z = invNorm(0.40) = -0.2534
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Find the corresponding "x" value:
x = z*+u
x = -0.2534*17.94 +98.09
x =93.54

#

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3)z = invNorm(0.38) = -0.3055
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Find the corresponding "x" value:
x = z*+u
x = -0.3055*4 +40
x =38.78

#percentile corresponding to p = 38% of the number of hours studying. is 38.78