Question: For a normally distributed random variable x with = 100 and = 16, use technology to find each probability. P(x > 100) P(x < 140)

For a normally distributed random variable x with = 100 and = 16, use technology to find each probability.

  1. P(x > 100)
  1. P(x < 140)
  1. P(92 < x < 108)
  1. P(x > 84)

In Mr. Church's class, the average amount of time spent studying for the final exam was 7.5 hours, with a standard deviation of 1.6 hours. Use technology to find each probability.

  1. What is the probability a randomly selected student spent at least 6 hours studying for the exam?
  1. What is the probability a randomly selected student spent no more than 4 hours studying for the exam?
  1. What is the probability a randomly selected student spent between 5 and 9 hours studying for the exam?
  1. What is the probability a randomly selected student spent less than 8 hours studying for the exam?

Solve the following.

  1. The weights of a sample of 30 potatoes from a farm are given below. If the mean is 0.49 lb and the standard deviation is 0.1 lb, does the data appear to be normally distributed? Explain.

  1. The heights of 24 children on a merry-go-round in a park are given below. If the mean of all the children at the park is 45 inches and the standard deviation is 6 inches, does the data appear to be normally distributed? Explain.

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