The tensile strength of spot welds produced by a robot welder is normally distri

Question

The tensile strength of spot welds produced by a robot welder is normally distributed, with a mean of 10,000 pounds per square inch and a standard deviation of 800 pounds per square inch. For a simple random sample of n = 4 welds, what is the probability that the sample mean will be at least 10,200 pounds per square inch?

A.0.6915 B.0.3085 C.0.4013 D.0.2500

Referring to the information in question 8, what is the probability that the sample mean will be less than 9900 pounds per square inch?

A.0.2500 B.0.3085 C.0.4013 D.0.6915

Explanation / Answer

answer first part)

here mean=10000, standard deviation=sd=800 and n=4

we go for standard normal variate z as the standard deviation of the population is given

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

for x=10200, z=(10200-10000)/(800/sqrt(4))=0.5

P(x<10200)=P(z<0.5)=0.6915 (using MS-excel command=normsdist(0.5))

answer is A.0.6915

answer second part)

for x=9900, z=(9900-10000)/(800/sqrt(4))=-0.25

P(x<9900)=P(z<-0.25)=0.4013(using MS-excel command=normsdist(-0.25))

answer is C.0.4013

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