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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 370g and a standard deviation of 24g. The amounts of raisins are also normally distributed with a mean of 170g and astandard deviation of 7g.Let T = the total amount of product in a randomly selected box, and assume that the amounts of flakes andraisins are independent of each other.Find the probability that the total amount of product exceeds 515g.You may round your answer to two decimal places.P(T > 515)=?

Respuesta :

Solution

For this case we can do the following:

X= amount of flakes

Y= amount of raisins

And for this case we have the following:

mu_x = 370, sd_x = 24

mu_y = 170, sd_x = 7

T = X+Y

And we want to find the following probability:

P( T> 515 gr)

The distribution of T is given by:

mu_T = 370 +170 = 540

[tex]sd_T=\sqrt[]{24^2+7^2}=25[/tex]

And we can use the z score to solve the problem on this way:

[tex]P(T>515)=1-P(T<515)=1-P(Z<\frac{515-540}{25})[/tex][tex]1-P(z<-1)=1-0.841=0.16[/tex]

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