统计学样本分布题目,英文,

题目

统计学样本分布题目,英文,
The mean of the weights of a large bunch of pencil is four times the standard
deviation.If the weights of these pencils are normally distributed and the
probability that the weight of a randomly chosen pencil is greater than 5 grams is
0.028.
a.Twenty of these pencils are chosen at random and the mean of the sample is
calculated.Find the probability that this mean is between 3 and 4 grams.

答案

Let the standard deviation be s,then the mean is 4s,and P(X>5)=0.028 that is P((X-4s)/s>(5-4s)/s)=0.028 where (X-4s)/s is standard normalCheck the standard normal table,(5-4s)/s=1.911,hence s=0.846The...