Question

Kwebwork/ spring201819-math242-bracey / latech stat ch4 /4 LaTech Stat Ch4: Problem 4 Prevous Problem Problern Lst Next Problerm s ont A son·ar nk bottler urchases ass bottes troma vendor. The bottles are required to have an internal pressure of at least í 50 pounds per square inch (psi). A bottler strikes an agreement with the vendor that permits the bottler to sample from the production process to verify the claim. the bottler randomly selects 60 bottles from the last 10000 produced, measures the internal pressure of each, and finds the mean pressure for the sample to be 0.8 psi below the process mean cited by the vendor. bottle vendor claims that its production process yields bottles with a mean internal pressure of 157 psi and a standard deviation of 3 psi. The (a) Assuming that the vendor is correct in his claim, what is the probability of obtaining a sample mean this far or farther below the process mean? (b) If the standard deviation were 3 psi as claimed, but the mean was 160 psl, what is the probablity of obtaining a sample mean of 156.2 psi or below? deviation was 1.4 psi, what is the probability of obtaining a sample mean of 156.2 psi or below? (c) If the process mean were 157 psi as claimed, but the standard Note: You can earn partial credit on this problem di

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	157
std deviation   =σ=	3.0000
sample size       =n=	60
std error=σx̅=σ/√n=	0.3873

probability =

P(X<156.2)

=

P(Z<-2.07)=

0.0192

(try 0.0194 if this comes wrong)

b)

probability =

P(X<156.2)

=

P(Z<-9.81)=

0.0000

c)

probability =

P(X<156.2)

=

P(Z<-4.43)=

0.0000