Normal Distributions, Exercises of Mathematics

worksheet on normal distributions

Typology: Exercises

2020/2021

Uploaded on 04/21/2025

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Normal Distribution Practice 7 Name __________________________________________
1. The mean life of a tire is 30,000 km. The standard deviation is 2000 km.
a) What percent of the tires will have a life that exceeds 25,000 km?
b) If a company purchased 2000 tires, how many tires would you expect to last more than 27 400 km?
2. The shelf life of a particular cheese is normally distributed with a mean of 12 days and a standard deviation of 3 days.
a) About what percent of the cheese last between 10 and 15 days?
b) About what percent of the cheese last between 13 and 16 days?
c) The oldest 10% of cheese are put on sale. These cheeses will be older than what age?
d) From a random selection of 60 cheeses, how many would you expect to be over a week old?
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Normal Distribution Practice 7 Name __________________________________________

  1. The mean life of a tire is 30,000 km. The standard deviation is 2000 km. a) What percent of the tires will have a life that exceeds 25,000 km? b) If a company purchased 2000 tires, how many tires would you expect to last more than 27 400 km?
  2. The shelf life of a particular cheese is normally distributed with a mean of 12 days and a standard deviation of 3 days. a) About what percent of the cheese last between 10 and 15 days? b) About what percent of the cheese last between 13 and 16 days? c) The oldest 10% of cheese are put on sale. These cheeses will be older than what age? d) From a random selection of 60 cheeses, how many would you expect to be over a week old?
  1. A line up for tickets to a local concert had a mean waiting time of 20 min with a standard deviation of 4 min. a) What percentage of the people in line waited for more than 28 minutes? b) If 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes?
  2. On a recent math test, the mean score was 75 and the standard deviation was 5. Mike made 93. Would his mark be considered unusual, if the marks were normally distributed? (Explain with calculations)
  3. In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 g. a) If 10,000 cookies were produced, how many cookies are within 5 g of the mean? b) Cookies are rejected if they weigh more than 44 g or less than 36 g. How many cookies would you expect to be rejected in a sample of 10,000 cookies?
  4. The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. a) What percentage of cars averaged less than 83 km/h? b) If a police car stopped cars that were going more than 104 km/h, how many cars would they stop if there were 8000 cars on the highway?

b) How many workers earn less than $750 per month? c) What percentage of the workers earn between $750 and $1500 per month? d) What percentage of the workers earns less than $1750 per month?

  1. Scores on the Wechsler Adult Intelligence Scale, a standard IQ test, are approximately normal for the 20 to 34 age group with μ = 110 and σ = 25. a) What percent of this age group have an IQ less than 100? b) What percent of this age group have an IQ between 90 and115? c) 80 % of the IQ scores are greater than what value? d) Find the IQ score which separates the lowest 25% of all IQ scores for this age group from the highest 75%.