can you help me solve for A) Average B) Standard deviation C) Probability Proble

Question

can you help me solve for A) Average B) Standard deviation C) Probability

Problem No. 2 a) A producer of mayonnaise uses jars in which to sell t. These jars are labeled as containing 16 oz. of mayonnaise. Government regulations require that a jar labeled indicating 16 oz. must contain at least 15.9 oz 96% of the time Also, the producer does not want to put any more mayonnaise in the jar than he has to. So he does not want exceed 16.32 oz more than 99% of the time. Determine the average setting of the dispensing machine and the standard deviation required to achieve the objectives. Calculate to the nearest 2 decimal places a) Average a) Standard deviation b)Probability b) Given your answers above, what percentage of the time will the jar overflow if it can contain 16.35 oz. at most? (0.5 points)

Explanation / Answer

here lets say the average is M and standard deviation is S.

so here

as per the question,

Pr(x > 15.9 oz) = 0.90

Pr(x <15.9 oz) = 0.10

NORM(x < 15.9 oz ; M ; S) = 0.10

here the Z value is

Z = -1.282 = (15.9 - M)/S

15.9 = M - 1.282 S ....(i)

now second condition is

Pr(x > 16.32 oz) = 1 - 0.99 = 0.01

Z = 2.575

(16.32 - M)/S = 2.575

16.32 = M + 2.575S

now solving these two equations

(2.575 + 1.282) S = (16.32 - 15.90)

S = 0.109 oz

M = 16.32 - 2.575 * 0.109 = 16.04 oz

(b) Probability of containing more than 16.35oz

Pr(x >16.35 oz ; 16.04 oz ; 0.109 oz)

Z = (16.35 - 16.04)/0.109 = 2.844

Pr(x >16.35 oz ; 16.04 oz ; 0.109 oz) = 1 - Pr(Z < 2.844) = 1 - 0.0022 = 0.9978

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