A breakfast cereal producer makes its most popular product by combining just raisins and flakes in each box of cereal. The amounts of flakes in the boxes of this cereal are normally distributed with a mean of 370 g 370g370, start text, g, end text and a standard deviation of 24 g 24g24, start text, g, end text. The amounts of raisins are also normally distributed with a mean of 170 g 170g170, start text, g, end text and a standard deviation of 7 g 7g7, start text, g, end text.

Complete question :

A breakfast cereal producer makes its most popular product by combining just raisins and flakes in each box of cereal. The amounts of flakes in the boxes of this cereal are normally distributed with a mean of 370 g and a standard deviation of 24 g. The amounts of raisins are also normally distributed with a mean of 170 g and a standard deviation of 7 g. Let T = the total amount of product in a randomly selected box, and assume that the amounts of flakes and raisins are independent of each other. Find the probability that the total amount of product is less than 575 g. You may round your answer to two decimal places. PT < 575)

0.91924

Step-by-step explanation:

Cereal :

X ~ N(μ = 370 ; σ² = 24²)

X ~ N(370 ; 576)

Raising :

X ~ N(μ = 170 ; σ² = 7²)

X ~ N(170 ; 49)

μ1 + μ2 = 370 + 170 = 540

σ1² + σ2² = 576 + 49 = 625

μ = μ1 + μ2 = 540

σ = sqrt(σ1² + σ2²) = 25

Recall:

Z = (x - μ) / σ

P( T < 575) = (575 - 540) / 25

P( T < 575) = 35 / 25

P( T < 575) = 1.4

P(Z < 1.4) = 0.91924

P(T>515)= .84

Step-by-step explanation:

Khan

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