Question

pom DevoPeStat9 5.E.504.XP. My Notes Ask Your Teacher breaking strength of a rivet has a mean value of 10,100 psi and a standard deviation of 499 psi. (a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 10,000 and 10,300? (Round your answer to four decimal places.) 0.0963 (b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your reasoning. Yes, the probability in part (a) can still be calculated from the given information No, n should be greater than 30 in order to apply the Central Limit Theorem No, n should be greater than 20 in order to apply the Central Limit Theorem. No, n should be greater than 50 in order to apply the Central Limit Theorem. may need to use the appropriate table in the Appendix of Tables to answer this question

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	10100
std deviation   =σ=	499.000
sample size       =n=	40
std error=σx̅=σ/√n=	78.8988

probability =

P(10000<X<10300)

=

P(-1.27<Z<2.53)=

0.9943-0.102=

0.8923

b)

No n should be greater than 30 to apply central limit theorem