Answer to Question #311241 in Statistics and Probability for Markskiegeee

Question

Suppose the mean number of days to germination of a variety of seeds is 34, with a standard deviation of 4.3 days. What is the probability that the mean germination time of a sample of 250 seeds will be within 0.5 days of the population mean?

Answer 1

$\sigma=4.3,\mu=34,n=250$

Standard deviation of sampling distribution $=\frac{sd}{\sqrt{n}}=\frac{4.3}{\sqrt{250}}=0.2720$

$P(\frac{-0.5}{0.2720}<Z<\frac{0.5}{0.2720})=P(-1.84<Z<1.84)$

$=P(Z<1.84)-P(Z<-1.84)=0.9671-0.0329$

$=0.9342$