A certain fruit’s weights are normally distributed, with a mean of 290 grams and a standard deviation of 33 grams. A random sample of 23 pieces of fruit is taken.

Question

(a) Describe the sample distribution of the sample means. 𝑋~N( ____ , ____ )

(b) If you pick 23 pieces of fruit at random then 13% of the time, their mean weight will be greater than how many grams?

Answer 1

X ~ N(290,33/square root(23))

z = (sample mean - population mean)/(population standard deviation/square root sample size)

= (sample mean - 290)/(33/square root (23)) = (sample mean - 290)/6,88)

Find z score corresponding to probability of 013 = -1.126

-1.126 = (sample mean - 290)/6.88

sample mean = 282.25 grams