Devry MATH221 Statistics for Decision Making Week 4 Homework
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 0.91, which is usual as it is greater 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%
Question 2Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. Find the probability that a randomly selected bill will have an amount greater than $165, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?
Probability is 0.06, which is unusual as it is not less than 5%
Probability is 0.06, which is usual as it is not less than 5%
Probability is 0.94, which is usual as it is greater than 5%
Probability is 0.94, which is unusual as it is greater than 5%
Question 3In 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.
0.40
Less than 1%
0.70
0.30
Question 4A 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 0.70mm. Would this outcome warrant a refund (meaning that it would be unusual)?
Probability of 0.79 and would not warrant a refund
Probability of 0.79 and would warrant a refund
Probability of 0.21 and would not warrant a refund
Probability of 0.21 and would warrant a refund
Question 5A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 7.45 minutes with a standard deviation of 2.81 minutes.
0.818
0.636
0.182
0.018
Question 6In an agricultural study, the average amount of corn yield is normally distributed with a mean of 185.2 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1100 acres, about how many would be expected to yield more than 190 bushels of corn per acre?
503 acres
419 acres
461 acres
639 acres
Question 7On 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 8A process is normally distributed with a mean of 10.6 hits per minute and a standard deviation of 0.49 hits. If a randomly selected minute has 11.8 hits, would the process be considered in control or out of control?
In control as this one data point is not more than three standard deviations from the mean
In control as only one data point would be outside the allowable range
Out of control as this one data point is more than three standard deviations from the mean
Out of control as this one data point is more than two standard deviations from the mean
Question 9The candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 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 two of these data points are more than 2 standard deviations from the mean
It is out of control as the values jump above and below the mean
It is out of control as at least two of three consecutive data points are more than 2 standard deviations from the mean
It is out of control as one of these data points is more than 3 standard deviations from the mean
Question 10The 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 5% of their toasters sold?
5.9 years
7.3 years
4.6 years
4.3 years