Flashcards
Summary Opmt1130
Cards in this deck (8)
- 1A telephone operator receives an average of 6 calls every 15 minutes. What is the probability that the operator will receive at least one call during the next 5 minutes?
- 2The records of a department store show that one out of every five customers who make a purchase return the merchandise in order to exchange it. (a) In the next 15 purchases, what is the probability at least two customers will return the merchandise for exchange? (b) In the next 100 purchases, what is the probability: (i) at least 25 customers will return the merchandise? (ii) 16 or fewer customers will?
- 3The Board of Directors at a financial institution is made up of 14 men and 6 women. A committee of three will be chosen at random from among the 20 directors. What is the probability that the three committee members are all the same gender?
- 4The annual salaries of recent business graduates are normally distributed with a mean of $40,000 and a standard deviation of $4,000. (a) What percentage earn: (i) at least $38,000? (ii) between $40,000 and $60,000? (b) The salaries earned by the middle 92% of recent graduates are between what two values? (c) 2 out of every 3 recent business graduates earn a salary higher than what amount? (d) If you take a random sample of 16 recent business graduates, what is the probability of obtaining a mean starting salary that is within $1,500 of the population mean salary? (e) 4% of recent graduates are married. If you take a random sample of 150 recent graduates, what is the probability that at least 10 among the 150 are married? (f) 4% of recent graduates earn less than $33,000. In a random sample of 150 recent graduates, what is the probability of at least 10 among the 150 earning less than $33,000?
- 5A bottling machine dispenses soft drink. The volume of soft drink that goes into a 12-ounce bottle is normally distributed with a mean of 12.60 ounces and standard deviation of 0.50 oz. (a) Consumer legislation states that 95% of bottles should contain at least 12 ounces (i.e. no more than 5% of bottles may contain less than the labelled volume of 12 ounces). Are the bottling machines in compliance with the law?
- 6You are conducting a poll to see whether cola-drinkers prefer Coke or Pepsi. A random sample of 400 cola-drinkers was polled and its results were that 280 preferred Coke. (a) What is the margin of error in the poll at a 95% level of confidence? (b) Construct a 95% confidence interval for the percentage of cola-drinkers who prefer Coke. (c) What sample size would you need to estimate the percentage of people who regularly drink coffee if you want the error on the estimate to not exceed 2% with 90% confidence?
- 7An electronics manufacturer is required to find the average lifetime of an expensive component. Because of the high cost of sampling it was decided to test only a sample of six components. From their sample they obtained a mean lifetime of 60 months and a standard deviation of 4.2 months. Assume the lifetimes of these components are normally distributed. (a) Construct a 95% confidence interval for the mean lifetime of a component in months. (b) The production manager decides the margin of error is too large. What sample size is needed to reduce the margin of error to one month with 95% confidence? Assume the sample standard deviation is a close estimate of the population standard deviation.
- 8Before September 11, 2001, 3 out of every 4 B.C. passenger vehicles that go south across the B.C.-Washington border on weekends are day-trippers, i.e., they go south, shop, and return to B.C. on the same day. After September 11, 2001, it is believed that this proportion has decreased. A sample of 120 B.C. passenger vehicles was taken on a weekend, and it is found that 78 of them were day-trippers. (a) Is there enough evidence to conclude the proportion of day-trippers has decreased since Sept. 11th, 2001? Test the hypotheses at the 2% level of significance. Your test must include the null and alternative hypotheses, a diagram, a decision rule, a decision with justification, and a conclusion. (b) Calculate the p-value.
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- BCIT (OPMT 1130) Flashcards on Summary Opmt1130, created by Praneil Kumar on 22/05/2017.
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