Answer to Question #139099 in Statistics and Probability for Archana jha

Question

In a sample of 1,000 items, the mean weight and
standard deviation are 45 kgs and 15 kgs respectively.
Assuming the distribution to be normal, find the number
of items weighing between 40 kgs and 60 kgs.
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Answer 1

We need to compute $P(40 \le \bar X \le 60)$. The corresponding z-values needed to be computed are:

$Z_1 = \frac{\bar X_1 - \mu}{\sigma}= \frac{ 40-45}{ 15} = -0.33$

$Z_2 = \frac{\bar X_2- \mu}{\sigma}= \frac{ 60-45}{ 15} = 1$

$P(40≤ \bar X ≤60)=P(-0.33≤Z≤1)=P(Z≤1)-P(Z≤-0.33)=0.84134-0.3707=0.4706$

Number of items N=n*P=100*0.57=470.6=471