Question

True or False: the central limit theorem states that the sampling distribution of the sample mean is approximately normal whenever the population from which we are sampling is normally distributed

Assume that 14% of the items produced in an assembly line operation are defective, but that the firm’s production manager is not aware of this situation. Assume firtber that the wuality assurance department to determine the quality of the assembly operation tests 50 parts. What is the probability that the sample will comtain at least 5 defective items?

Answer 1

the central limit theorem states that the sampling distribution of the sample mean is approximately normal whenever the population from which we are sampling is normally distributed

TRUE

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Sample size , n = 50

Probability of an event of interest, p =0.14

and probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

P(X≥5) = 1 - [ P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) ] = 0.8472(answer)

probability that the sample will comtain at least 5 defective items = 0.8472