The masses of cans of Milo are known to have a Normal distribution with mean 755

Question

The masses of cans of Milo are known to have a Normal distribution with mean 755 grams and standard deviation 1.05 grams. Using the Normal probability table from the notes, calculate the following: (a) the probability that the mas of a Milo can is less than 756 grams (2 marks) (b) the probability that the mass of a Milo can is at least 756 grams (2 marks); (c) the probability that the mass of a Milo can is between 756 and 757 grams (3 marks): (d) the value of the mass so that at most 1.52% of the cans exceed this mass (3 marks) For each of (a- include a diagram in your answer wih the given noaone value you are trying to find clearly marked.

Explanation / Answer

Params of normal dist have been given as Mean = 755, Stdev = 1.05

We will use them to standardize our distribution as follows:

a. P(X<756) = P(Z< 756-755 / 1.05) = P(Z<1/1.05) = .748)

b. P(X>=756) = 1-P(X<756) = 1-.748 = .252

c. P(756<X<757) = P(1/1.05 <Z< 2/1.05) = .9088-.7475 = .1613

d. P(x>=c) = .0152, because we have find c such that only .0152 of Milo mass is above it.

So, lets take Z value for P(X>=c) =.0152 , So, Z = 2.165
Hence, Milo mass =c = Mean+2.165*stdev = 755+2.165*1.05 = 757.2733

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