Statistics problem on weights

Assume the weight of a product is normally distributed with a meanof 1.5 and a varianceof 0.2.
What percentage of products will have weights within +/- 3 standard deviations?
What are the lower and upper limits bounding 50% of product weights?
Determine the weight where no more than 1% of all products will exceed that amount.

Assume the weight of a product is normally distributed with a mean of 1.5 and a variance of 0.2.
What percentage of products will have weights within +/- 3 standard deviations?

Solution. Let X be the weight. Then X follows a normal distribution with mean mu=1.5 and variance of 0.2. So, the standard deviation is sigma=root of 0.2=0.45. Then X~N(1.5, 0.45).

Let Z=(X-1.5)/0.45. Then Z~N(0, …

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