c. IfI weighed 15 pounds more than I do, what percentile would I be in A product

Question

c. IfI weighed 15 pounds more than I do, what percentile would I be in A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation 0.1. An item is considered to be defective if its weight is less than 9.8 pounds or greater than 10.2 pounds. Suppose that these items are currently produced in batches of 1000 units. a. Find the probability that at most 5% of the items in a given batch will be defective b, Oind the probability that at least 85% of these items in a given batch will be acceptable. Mathematical Statistics SaluionsProbabilitya Solutions Probability and with Statistics for

Explanation / Answer

Ans:

Mean=10

std deviation=0.1

z=(9.8-10)/0.1=-2

z=(10.2-10)/0.1=2

P(z<=-2)+P(z>=2)=2*0.02275=0.0455

4.55% are defective or 95.45% are acceptable.

sampling distribution of proportions:

a)n=1000

p=0.0455

z=(0.05-0.0455)/sqrt((0.0455*0.9545)/1000)

=0.6828

P(z<=0.6828)=0.7526

b)p=1-0.0455=0.9545

z=(0.85-0.9545)/sqrt((0.0455*0.9545)/1000)=-15.86

P(z>=-15.86)=1-P(z<-15.86)=1-0=1

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