The weight of a product is normally distributed with a mean of 4 ounces and a variance of .25 squared ounces. What is the probability that a

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The weight of a product is normally distributed with a mean of 4 ounces and a variance of .25 squared ounces. What is the probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces

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Acacia 3 years 2021-08-26T04:08:17+00:00 1 Answers 29 views 0

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  1. thanhha
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    2021-08-26T04:10:05+00:00
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    Answer: 0.0228

    Step-by-step explanation:

    Let x be the weight of a product.

    The probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces:

    P(X>5)\\\\=P(\dfrac{X-Mean}{\sqrt{Variance}}>\dfrac{5-4}{\sqrt{0.25}})\\\\=P(Z>\dfrac{1}{0.5}) \ \ \ [z=\dfrac{X-Mean}{\sqrt{Variance}}]\\\\=P(z>2)\\\\=1-P(Z<2)\\\\=1-0.9772\ \ [\text{Using p value table}]\\\\=0.0228

    Hence, the required probability = 0.0228

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