QUESTION 5. Company X wants to procure products from two different suppliers it has determined, but...

QUESTION 5. Company X wants to procure products from two different suppliers it has determined, but has doubted the quality of these suppliers' products. For this reason, he took random samples from both suppliers before placing their exact orders. He bought 50 products randomly from supplier A, and their average survival time was 153 hours and standard deviation was 10 hours. The average duration of 50 products bought from supplier B was 150 hours and the standard deviation was 5 hours. Accordingly, what is the probability that the difference between the two suppliers' durability of their products will be more than 7 hours?

Solutions

Expert Solution

We have Xa = 153, Sa = 10, na = 50

Xb = 150, Sb = 5, nb = 50

The difference bwtween the two suppliers' durability of their products will be more than 7 hours, so D = 7

Here X is average sample survival time and S is the sandard deviation, n is the number of products

Z-score = (Xa - Xb - D) / Sa2 / na + Sb2 / nb

= (153 - 150 - 7) / 102 / 50 + 52 / 50

= -3 / 2 + 1/2

= -3/ 2.5

= -3 / 1.5811

= -1.89737

Now we will calculate the p-value from the z-score

p-value will be area to the left of z-score which can be calculated from the negative z-table attached below

p-value for z-score of -1.90 the nearest z-score to -1.89737 is 0.02872.

But as we know that the p-value is the area to the left of z-score. So it is P(D<7), but we want P(D>7)

P(D>7) = 1 - P(D<7)

= 1 - 0.02872

= 0.97128 approximately

probability that the difference between the two suppliers' durability of their products will be more than 7 hours is 0.97128

orchestra answered 1 year ago

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