Question

Assume after much investigation it was found through chemical analysis of 1000 airbags, taken from five to ten year old cars in Houston Texas, that the average mass of the aged gas propellant mixture on the driver side was 55.9g with a standard deviation of 0.9g. It was also determined that those airbags that killed or injured the driver through flying debris had a mass over 59.5g.

a. What is the probability that a randomly obtained airbag from a nine year old vehicle in Houston Texas has an airbag that could kill its driver?

b.If the manufacture determined that aged airbags with propellant between masses of 57 and 58 should be replaced within the next 6 months, what percentage of five to ten year old vehicles in Houston Texas would be expected to fall into this category?

c. If the manufacturer determined that aged airbags with propellant with a mass greater than 59 must be replaced as soon as possible, what percentage of five to ten year old Houston Texas vehicles would be expected to fall into this category?

Answer 1

To solve this question, we are assuming that the mass of the aged gas propellant mixture on the driver side of the airbag, taken from five to ten-year-old cars in Houston Texas, follows a normal distribution. Let the same be denoted by X.

Then

X ~ Normal(55.9,0.9)

a.

The following information has been provided:

μ=55.9, σ=0.9

We need to compute The corresponding z-value needed to be computed is:

Therefore, we get that

b.

c.

We need to compute . The corresponding z-value needed to be computed is:

Therefore, we get that

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