Answer to Question #307862 in Statistics and Probability for jane

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

we define the following

mean = 34

standard deviation = 4.3

standard deviation of the sampling distribution=(standard deviation) / ((n)^1/2)

Thus

standard deviation of the sampling distribution= (4.3) / ((250)^1/2) = 0.271955878

Probability= P ( ( (-0.5)/(0.271955878) ) < Z< ( (-0.5)/(0.271955878) ) )

the above yields

Probability = P(-1.84<Z< 1.84) = P(Z<1.84) - P(z<-1.84)

using the normal tables we have that

Probability = (0.96712) - (0.03288) = 0.93424 which is the required solution.