Devry MATH221 Week 4 Homework Latest 2021 June

MATH221 Statistics for Decision Making

Week 4 Homework

Question 1The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?

  Probability is 0.09, which is unusual as it is less than 5%

  Probability is 0.09, which is usual as it is not less than 5%

  Probability is 0.91, which is unusual as it is greater than 5%

  Probability is 0.91, which is usual as it is greater than 5%

 Question 2In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

  Less than 1%

  0.70

  0.30

  0.40

 Question 3A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.50mm. Would this outcome warrant a refund (meaning that it would be unusual)?

  Probability of 0.91 and would warrant a refund

  Probability of 0.91 and would not warrant a refund

  Probability of 0.09 and would not warrant a refund

  Probability of 0.09 and would warrant a refund

 Question 4In an agricultural study, the average amount of corn yield is normally distributed with a mean of 189.3 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 180 bushels of corn per acre?

  785 acres

  654 acres

  346 acres

  415 acres

 Question 5On average, the parts from a supplier have a mean of 31.8 inches and a standard deviation of 2.4 inches. Find the probability that a randomly selected part from this supplier will have a value between 27.0 and 36.6 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?

 Probability is 0.95, which is consistent with the Empirical Rule

  Probability is 0.02, which is inconsistent with the Empirical Rule

  Probability is 0.98, which is inconsistent with the Empirical Rule

  Probability is 0.95, which is inconsistent with the Empirical Rule

Question 6A process is normally distributed with a mean of 10.2 hits per minute and a standard deviation of 1.04 hits. If a randomly selected minute has 12.9 hits, would the process be considered in control or out of control?

  In control as only one data point would be outside the allowable range

  Out of control as this one data point is more than two standard deviations from the mean

  Out of control as this one data point is more than three standard deviations from the mean

  In control as this one data point is not more than three standard deviations from the mean

 Question 7The candy produced by a company has a sugar level that is normally distributed with a mean of 16.8 grams and a standard deviation of 0.9 grams. The company takes readings of every 10th bar off the production line. The reading points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 19.4. Is the process in control or out of control and why?

  It is out of control as the values jump above and below the mean

  It is out of control as two of these data points are more than 2 standard deviations from the mean

  It is in control as the data points more than 2 standard deviations from the mean are not among three consecutive data points

  It is in control as only one of these data points is more than 3 standard deviations from the mean

 Question 8The toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, what warranty should be provided so that the company is replacing at most 10% of their toasters sold?

  4.6 years

  4.5 years

  5.9 years

  4.3 years

 Question 9A running shoe company wants to sponsor the fastest 3% of runners. You know that in this race, the running times are normally distributed with a mean of 7.2 minutes and a standard deviation of 0.56 minutes. How fast would you need to run to be sponsored by the company?

  8.1 minutes

  6.3 minutes

  6.1 minutes

  8.3 minutes

 Question 10A stock’s price fluctuations are approximately normally distributed with a mean of $29.51 and a standard deviation of $3.87. You decide to sell whenever the price reaches its highest 20% of values. What is the highest value you would still hold the stock?

  $32.77

  $32.38

  $24.50

  $25.25

 Question 11In a survey of first graders, their mean height was 50.4 inches with a standard deviation of 3.55 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?

  48.01 inches

  43.30 inches

  52.79 inches

  46.84 inches

Question 12Hospital waiting room times are normally distributed with a mean of 38.12 minutes and a standard deviation of 8.63 minutes. What is the shortest wait time that would still be in the worst 15% of wait times?

  29.18 minutes

  36.49 minutes

  47.06 minutes

  49.18 minutes

Question 13The length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches. In a random sample of 45 boards, what is the probability that the mean of the sample will be between 94.5 inches and 95.1 inches?

  0.591

  0.009

  0.408

  0.901

Question 14Of all the companies on the New York Stock Exchange, profits are normally distributed with a mean of $6.54 million and a standard deviation of $10.45 million. In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between 0 million and 5.1 million?

  0.012

  0.120

  0.105

  0.015

 Question 15Doing research for insurance rates, it is found that those aged 30 to 49 drive an average of 38.7 miles per day with a standard deviation of 6.7 miles. These distances are normally distributed. If a group of 60 drivers in that age group are randomly selected, what is the probability that the mean distance traveled each day is between 38.0 miles and 39.9 miles?

  0.199

  0.708

  0.780

  0.113