A= B= C= Answer: A= Furniture manufacturing companies often deal with the qualit

Question

A=

B=

C=

Answer:

A=

Furniture manufacturing companies often deal with the quality of the drilling of dowel holes. Consider the case of Company X. which believes that when the drilling process is operating at an acceptable rate. the upper limit on the percentage of incorrectly drilled do wel holes is 8%. To monitor its drilling process, the company randomly samples 14 products each hour and determines if the dowel hole in each product is correctly drilled or not. If, in the sample of 14 holes, 1 or more incorrectly drilled holes is discovered, the production process is stopped and the drilling process is recalibrated. Use this information to complete parts a through c a. If the process is really operating correctly (p -0.08). what is the probability that the sampling effort will produce x O defective holes and thus the process will properly be left to continue running? Round to four decimal places as needed

Explanation / Answer

Let's write the given information

n = sample size = 14, probability of incorrectly drilled drowel holes = 0.08

a) we want to find P(X = 0)

Where X is a random variable which takes values of incorrectly drilled drowel holes.

By using excel command as =BINOMDIST(numbers, trial, probability, cumulative) we can find the above probability

Here we need to put number = X = 0, trials = n = 14, probability = p = 0.08 and cumulative =0

That is we used "=BINOMDIST(0,14,0.08,0)" and then enter .

we get P(X = 0) = 0.3112

b) For p=0.10 we have to find P(X >= 1) because if there 1 or more than 1 defectives in the sample then we recallibrate the drilling machine.

So P(X >= 1) = 1 - P(X = 0)

first we need to find P(X = 0) using the excel command as "=BINOMDIST(0,14,0.1,0)"

So we get P(X = 0) = 0.2288

Therefore P(X >= 1) = 1 - P(X = 0) = 1 - 0.2288 = 0.7712 (this is the final answer of part b)

c) When assuming that the process operating correctly that is p= 0.08 then

P(X >= 1) = 1 - P(X = 0) =1 - 0.3112 = 0.6888 this is the probability that the sample leads to the production process being stop, which is very high

When assuming that the process operating not correctly then p = 0.10

the probability that the sample does not leads to the production process being stop is

P(X = 0) = 0.2288 which is farly low.

For the next question we have

n = sample size = 50, p = 0.69

For the phrase fever than we used < inequality.

So here we need to find P(X < 29) = P(X <= 28)

We convert it into less than or equal to form because excel binomial command provide less than or equal probability.

So the command is "=BINOMDIST(28,50,0.69,1)"

P(X <= 28) = P(X < 29) = 0.0360 (this is the final answer of part a)

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