Question

Eurowatch company assembles expensive wristwatches and then sells them to retailers throughout europe. The watches are assembled at a plant with two assembly lines. These lines are intended to be identical, but line 1 uses somewhat older equipment than line 2 and is typically less reliable. Historical data have shown that each watch coming off line 1, independently of the others, is free of defects with probability .98. The similar probability for line 2 is 0.99. Each line produces 500 watches per hour. The production manager has asked you to answer the following questions.

[1] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is greater than 500? 25% 100% 0% 50%

[2] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is less than 700? 0.4772 0.9772 almost 0 0.0228

[3] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is greater than 700? almost 0 0.9772 0.4772 0.0228

[4] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is between 300 than 700? 0.9545 almost 0 0.4545 0.0455

[5] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is less than 300 or more than 700? 0.9545 almost 0 0.0455 0.4545

Answer 1

First four questions have been solved in detail

[1] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is greater than 500?

[2] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is less than 700?

3] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is greater than 700?

[4] Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that in a randomly selected hour the number of watches produced is between 300 than 700?