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.
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.
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.
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.
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.
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?
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.
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?

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