statistics

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Answer the following: a. Find the uniform continuous probability for P(X < 8) for U(0, 50). (Round your answer to 2 decimal

places.)

Probability b. Find the uniform continuous probability for P(X > 580) for U(0, 1,000). (Round your answer to 3

decimal places.)

Probability c. Find the uniform continuous probability for P(30 < X < 51) for U(16, 60). (Round your answer to 4 decimal places.)

Probability

References

Worksheet Difficulty: 1 Easy Learning Objective: 07-02 Calculate uniform probabilities.

Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 1,516 pounds to 4,661 pounds. (a) What is the mean weight of a randomly chosen vehicle? (Round your answer to the nearest whole

number.)

Mean weight (b) What is the standard deviation of a randomly chosen vehicle? (Round your answer to 4 decimal

places.)

Standard deviation (c) What is the probability that a vehicle will weigh less than 1,753 pounds? (Round your answer to 4

decimal places.)

Less than 1,753 pounds

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(d) What is the probability that a vehicle will weigh more than 3,666 pounds? (Round your answer to 4

decimal places.)

More than 3,666 pounds (e) What is the probability that a vehicle will weigh between 1,753 and 3,666 pounds? (Round your answer

to 4 decimal places.)

Between 1,753 and 3,666 pounds

References

Worksheet Difficulty: 2 Medium Learning Objective: 07-02 Calculate uniform probabilities.

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 320 grams and a standard deviation of 14 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.) a. Highest 30 percent b. Middle 70 percent to c. Highest 90 percent d. Lowest 20 percent

References

Worksheet Difficulty: 2 Medium Learning Objective: 07-05 Solve for z or x for a given normal probability using tables or Excel.

The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 620 and a standard deviation of 90. (a) Find the credit score that defines the upper 20 percent. (Use Excel or Appendix C to calculate the z-

value. Round your final answer to 2 decimal places.)

Credit score

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(b) Eighty-five percent of the customers will have a credit score higher than what value? (Use Excel or

Appendix C for calculation of z-value. Round your final answer to 2 decimal places.)

Credit score (c) Within what range would the middle 90 percent of credit scores lie? (Use Excel or Appendix C for

calculation of z-value. Round your final answer to 2 decimal places.)

Range to

References

Worksheet Difficulty: 2 Medium Learning Objective: 07-05 Solve for z or x for a given normal probability using tables or Excel.

The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 573 MPa with a standard deviation of 11 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 573 MPa? (Round

your answer to 2 decimal places.)

Probability (b) What is the probability that a randomly chosen sample of glass will break at more than 589 MPa?

(Round your answer to 4 decimal places.)

Probability (c) What is the probability that a randomly chosen sample of glass will break at less than 596 MPa? (Round

your answer to 4 decimal places.)

Probability

References

Worksheet Difficulty: 2 Medium Learning Objective: 07-04 Find the normal probability for a given z or x using tables or Excel.

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If the weight (in grams) of cereal in a box of Lucky Charms is N(470,4), what is the probability that the box will contain less than the advertised weight of 458g? Note: You may need to use Excel to calculate the exact probabilities. (Round your answer to 5 decimal places.) Probability

References

Worksheet Difficulty: 1 Easy Learning Objective: 07-04 Find the normal probability for a given z or x using tables or Excel.