The average weight of a particular box of crackers is 28.0 ounces with a standard deviation of 0.9 ounce. The weights of the boxes are normally distributed. a. What percent of the boxes weigh more than 26.2 ounces?

Question

Mathematics

Adriana Camacho

1 January, 02:41

The average weight of a particular box of crackers is 28.0 ounces with a standard deviation of 0.9 ounce. The weights of the boxes are normally distributed. a. What percent of the boxes weigh more than 26.2 ounces?

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Answers (1)

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Humberto Sexton · Answer 1

a. 97.72%

Step-by-step explanation:

The weights of boxes follows normal distribution with mean=28 ounce and standard deviation=0.9 ounces.

a. We have to calculated the percentage of the boxes that weighs more than 26.2 ounces.

Let X be the weight of boxes. We have to find P (X>26.2).

The given mean and Standard deviations are μ=28 and σ=0.9.

P (X>26.2) = P ((X-μ/σ) > (26.2-28) / 0.9)

P (X>26.2) = P (z> (-1.8/0.9))

P (X>26.2) = P (z>-2)

P (X>26.2) = P (0
P (-2
P (X>26.2) = 0.5+0.4772

P (X>26.2) = 0.9772

Thus, the percent of the boxes weigh more than 26.2 ounces is 97.72%