8.9 Normal Distribution

The length of time that patients have to wait in the waiting room at Dr. Sattler's office is known to be normally distributed with mean 14 minutes, and standard deviation 4 minutes. Find the probability that a random patient will have to wait between 10-15 minutes to see the doctor. Write your answer as a percentage rounded to the nearest whole number.

Shade the region that represents about 68% of the data. Each dotted line represents a standard deviation.

Mr. Sattler discovers that the lifetime of washing machines is normally distributed with a mean of 8 years and standard deviation 2 years. What is the probability that a machine lasts longer than 10 years?

• about 16%

• about 68%

• about 95%

• about 2.5%

Robert Lewandowski discovers that the number of nuts in a bag of cashews is normally distributed with mean 42 and standard deviation 4. If he buys 200 bags, how many bags can he expect to contain fewer than 42 nuts?

• about 5 bags

• about 190 bags

• about 26 bags

• about 100 bags

Households in Portugal spend an average of 100 euro per week on groceries with a standard deviation of 20 euro. Assuming the distribution is normal, what is the probability that a household spends less than 130 per week? Write your answer as a decimal rounded 3 sf.

In Spanish La Liga for 2022/2023, it was calculated that the average points scored is 47 with a standard deviation of 15.24. Assuming the data is normally distributed, about how many teams scored below 35 points if there are 20 teams in the league?

Given a random variable X is normally distributed with mean 20, and the area of the shaded region is 0.2. Find P(X>10)

The mean weight of students at ICSV is 70kg, with standard deviation 6kg. About 95% of students weigh between X and Y. Find X and Y.

• X=58

  Y=82

• X=64

  Y=76

• X=70

  Y=82

• X=76

  Y=88

The random variable X is normally distributed with a mean of 90. The area of R is 0.22. Find P(84 < X < 90). Give your answer as a decimal.

The random variable X is normally distributed with a mean of 90. The area of R is 0.22. Find P(84 < X < 96). Give your answer as a decimal.