The cutting tools manufactured by Fox Company for industrial purposes had an ave

Question

The cutting tools manufactured by Fox Company for industrial purposes had an average lifetime of 220 days and standard deviation of 15 days.

a) A potential buyer intends to take a sample of sixty-four such cutting tools and will notplace an order if the sample mean is less than 215 days. What is the probability that the buyer will not place an order?

b) You intend to buy the tools from this company. You sample thirty cutting tools and willplace an order if the sample mean is at least 235 days. What is the probability that you will place an order?

Explanation / Answer

Here, n = 64 , mean = 220 , std. deviation = 15

a) p(X < 215)

By normal distribution formula,

z = (x - mean ) / (s / sqrt(n))

= ( 215-220) / ( 15 / sqrt(16))

= -1.33

Now, we need to find P(Z < -1.33)

P(x < 215 ) = P(Z < -1.33) = 0.0038

.0038 i s the  probability that the buyer will not place an order

b ) Here, n = 30

p(X > 235)

By normal distribution formula,

z = (x - mean ) / (s / sqrt(n))

= ( 235 - 220) / ( 15 / sqrt(30))

= 5.47

Now, we need to find P(Z > 5.47)

P(x > 235 ) = P(Z > 5.47) = 0

0 is the  probability that the buyer will place an order

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