The useful life of a radial tire is normally distributed with a mean of 30,000 miles and a standard deviation of 5000 miles. The company makes 10,000 tires a month. What is the probability that if a radial tire is purchased at random, it will last
between 20,000 and 35,000 miles?

  empirical rule: 81.5%

  table or calculator: 81.9%

Step-by-step explanation:

The lower limit of the life range of interest has a z-score of ...

  z = (x -μ)/σ = (20,000 -30,000)/5,000 = -2

The upper limit has a z-score of ...

  z = (35,000 -30,000)/5,000 = 1

Empirical rule solution

The empirical rule tells you that 95% of the distribution lies within 2 standard deviations of the mean, so (100% -95%)/2 = 2.5% lie below z = -2. It also tells you 68% lie within 1 standard deviation of the mean, so (100% -68%)/2 = 16% lie above z = 1.

The fraction that lies within -2 to 1 standard deviations of the means is thus ...

  (100% -2.5% -16%) = 81.5%

The probability the tire has a life in the desired range is about 81.5%.

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Calculator solution

A probability calculator for the Normal distribution tells you that ...

  P(-2 < z < 1) ≈ 0.8185946

The probability the tire has a life in the desired range is about 81.9%.

step-by-step explanation: 4 cause 2+2=4

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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