1. A major tire manufacturer sends out a recall for a particular tire it makes b

Question

1. A major tire manufacturer sends out a recall for a particular tire it makes because 2% of these tires are defective.

If you take a random sample of 600 of these tires, what is the probability that more than 3% of your sample is defective?

2.

Wildlife biologists believe that weights of adult trout are Normally distributed with a mean weight of 3 pounds and a standard deviation of 1.3 pounds.

What is the probability that a random sample of 15 adult trout has a mean weight more than 2.3 pounds?

Due to the different methods, round your answer to 2 decimal places.

Explanation / Answer

1.
Mean value of defective tires, lambda = 2% * 600 = 12
std.dev. = sqrt(600 * 0.02 * 0.98) = 3.4293
xbar = 600*0.03 = 18

Uning central limit theorem,
z = (18 - 12)/3.43 = 1.7493

P(Z > 1.7493) = 0.04

Hence option A is correct

2.
mean = 3
std. dev. = 1.3
SE = 1.3/sqrt(15) = 0.3357

Uning central limit theorem,
z = (2.3 - 3)/0.3357 = -2.0852

P(Z > -2.0852) = 0.98

Option A is correct

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