神马作文网统计学样本分布题目,英文,
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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.
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.
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 normal
Check the standard normal table,(5-4s)/s=1.911,hence s=0.846
The sample mean of twenty pencils is normally distributed with mean 4s=3.384 and standard deviation s/√20=0.189.
Then P(3
P(X>5)=0.028 that is P((X-4s)/s>(5-4s)/s)=0.028 where (X-4s)/s is standard normal
Check the standard normal table,(5-4s)/s=1.911,hence s=0.846
The sample mean of twenty pencils is normally distributed with mean 4s=3.384 and standard deviation s/√20=0.189.
Then P(3