A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the variable ? = actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 15.0 gallons and standard deviation 0.1 gallon.What is the probability that a randomly selected tank will hold at most 14.8 gallons?What is the probability that a randomly selected tank will hold between 14.7 and 15.1 gallons?If two such tanks are independently selected, what is the probability that both hold at most 15 gallons?

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Asked Dec 14, 2019
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  1. A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the variable ? = actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 15.0 gallons and standard deviation 0.1 gallon.

    1. What is the probability that a randomly selected tank will hold at most 14.8 gallons?

    2. What is the probability that a randomly selected tank will hold between 14.7 and 15.1 gallons?

    3. If two such tanks are independently selected, what is the probability that both hold at most 15 gallons?

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Expert Answer

Step 1

It is given that the actual capacity of a tank follows normal distribution with mean 15.0 gallons and standard deviation 0.1 gallon.

Denote the random variable X as the capacity of a randomly selected tank.

That is, µ= 15, σ = 0.1.

Thus, X~ N (15, 0.1).

1.

The probability that randomly selected tank will hold at most 14.8 gallons is calculated as follows:

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using EXCEL formula, P(X <14.8) = 0.0228| "ENORM.DIST(14.8,15,0.1,1)"

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Step 2

2.

The probability that randomly selected tank will hold is between 14...

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P(14.7<X<15.1) = 0.8413 – 0.0013 using EXCEL formula, = 0.8400 "=NORM.DIST(15.1,15,0.1,1)" "ENORM.DIST(14.7,15,0.1,1)"|

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