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

Makhi Perry

Mathematics

14 October, 01:40

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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Rosario · 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%