Question

MATH225 Statistical Reasoning for the Health Sciences

Week 5 Assignment Applications of the Normal Distribution

Question The number of walnuts in a mass-produced bag is
modeled by a normal distribution with a mean of 44and a standard
deviation of 5. Find the number of walnuts in a bag that has more
walnuts than 80% of the other bags.

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Use Excel, and round your answer to the nearest integer.

Question A firm’s marketing manager believes that total sales
for next year will follow the normal distribution, with a mean of
$3.2 million and a standard deviation of $250,000. Determine the
sales level that has only a 3% chance of being exceeded next year.

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Use Excel, and round your answer to the nearest dollar.

Question A certain type of mango that weighs over 450 grams
is considered to be large in size. The weights for this certain
type of mango, X grams, are normally distributed with a mean of 400
and a standard deviation of 20. Find the probability that a mango
of this type, selected at random, will not be considered as large.

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Round your answer to four decimal places.

Question A worn, poorly set-up machine is observed to produce
components whose length X follows a normal distribution with mean
14 centimeters and variance 9. Calculate the probability that a
component is at least 12 centimeters long.

•
Round your answer to four decimal places.

Question In a survey of men aged 20-29 in a country, the mean
height was 73.4 inches with a standard deviation of 2.7 inches.
Find the minimum height in the top 10% of heights.

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Use Excel, and round your answer to one decimal place.

Question Two thousand students took an exam. The scores on
the exam have an approximate normal distribution with a mean of
μ=81 points and a standard deviation of σ=4 points. The middle
50%of the exam scores are between what two values?

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Use Excel, and round your answers to the nearest integer.

Question On average, 28 percent of 18 to 34 year olds check
their social media profiles before getting out of bed in the
morning. Suppose this percentage follows a normal distribution with
a random variable X, which has a standard deviation of five
percent. Find the probability that the percent of 18 to 34 year
olds who check social media before getting out of bed in the
morning is, at most, 32.

•
Round your answer to four decimal places.

Question Sugar canes have lengths, X, that are normally
distributed with mean 365.45 centimeters and standard deviation 4.9
centimeters. What is the probability of the length of a randomly
selected cane being between 360 and 370 centimeters?

•
Round your answer to four decimal places.

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