Please show all work and explanation to Receive FULL CREDIT

Please show all work and explanation to Receive FULL CREDIT!!!

Your company produces sandblasting media in 100 lbs. bags. Your filling machinery can be adjusted to set the mean fill weight, normally distributed with a standard deviation of 0.5 lbs.

A. What is the probability of seeing a bag that weights exactly 100 lbs.?

B. To ensure customer satisfaction, you want to adjust the mean fill weight so that 99% of all bags will weigh at least 100 lbs. What value should you set the mean fill weight to?

Solution

(A) The probability is

P(X=100)= P(99.5<X<100.5)

=P((99.5-100)/0.5 <(X-mean)/s <(100.5-100)/0.5)

=P(-1<Z<1)

= 0.6827 (from standard normal table)

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(B) Z(0.99) =2.33 (from standard normal table)

So X = mu+Z*s = 100+2.33*0.5 =101.165