Use the following information to answer questions #21 through #25: A factory pro

Question

Use the following information to answer questions #21 through #25: A factory produces car tires. The number of miles each tire lasts before it completely wares out follows a normal distribution with mean 40,000 miles and standard deviation 25,000 miles. 1Oaa 21. What is the z-score for x = 45,500? C. 1.1 22. What is the probability for a randomly selected tire to last more than 45,500 miles, i.e., P(x 2 45,500)? A. 0.864 B. 0.364 © 0.136 D. 0.159 23. If the tires last for less than 30,000 miles, customers will complain. What is the probability for a randomly selected tire to last less than 30,000 miles, i.e. P(x S 30,000)? A. 0.9772 B. 0.4772 0.0455 0.0228 24. Suppose that the factory promises to the consumers that the tires will last for at least 40,000 miles. What is the probability for a randomly selected tire to last for at least 40,000 miles, i.e., P(x 2 40,000)? A 1.000 0.500 C.-0.500 D. 0.0228

Explanation / Answer

21. z - score = (45500 - 40000)/5000 = 1.1

Option C is correct.

22. P(X > 45500)

= P(z > (45500 - 40000)/5000)

= P(z > 1.1)

= 0.136

Option C is correct.

23. P(X < 30000)

= P(z < (30000 - 40000)/5000)

= P(z < -2)

= 0.0228

Option D is correct.

24. P(X > 40000)

= P(z > 0)

= 0.5

Option B is correct.

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