Kndly make the Answers Typed please Normal Distribution a. A machine fills 24-ou

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Kndly make the Answers Typed please

Normal Distribution

a. A machine fills 24-ounce (according to the label) boxes with cereal. The amount deposited into the box is normally distributed with a standard deviation of 0.20 ounce. What does the mean have to be in order for only 0.2% of the boxes to contain more than 24.5 ounces or more of cereal?

b. A student gets a 70 on a test where the mean score was 64. What does the standard deviation have to be in order for the student to be in the 95th percentile?

c. A machine fills 24-ounce (according to the label) boxes with cereal. The amount deposited into the box is normally distributed with a mean of 24.8 ounces. What does the standard deviation have to be in order for 96% of the boxes to contain 24 ounces or more?

d. On a standardized test, scores are normally distributed with a mean of 400 and a standard deviation of 80. What score must one have to be in the 80th percentile

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Explanation / Answer

a) use NORM.S.INV(0.002) in excel, so we get -2.87816

z=x-mu/sd

2.87816=24.5-mu/0.2

simplifying for mu we get 23.9243

b) 95th percentile coressponds to z=1.645

z=70-64/sd

1.645=6/sd

sd=6/1.645=3.64774

c) use NORMSINV(0.96) we get -1.7506

-1.7506=24-248/sd

sd=-0.8/-1.7506=0.4569

d) use NORMSINV(0.8) in excel, we get 0.841621,

0.841621=x-400/80

x=467.3297

c)

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