#### STAT 2606 E: Business Statistics I Assignment 3

- Description

**STAT 2606 E: Business Statistics I**

**Assignment 3**

**Due in Class Thursday, March 1, 2018**

**INSTRUCTIONS:**

- Assignments are to be handed in prior to beginning of class on the due date.
- For written questions, show all of your work. No credit will be given for answers without justification.

- Do not use MINITAB for a question unless it specifically says to do so. No late assignments will be accepted.
- During off hours, cars arrive at a highway service station at an average rate of 5 cars per10 minutes. The number of cars arriving at the service station is distributed according to a Poisson distribution.
- What is the probability that during the next minute three cars will arrive?
- What is the probability that during the next five minutes three cars will arrive?
- What is the probability that during the next five minutes at least two cars will arrive?

- Suppose that the times required for a cable company to fix cable problems in its customers’homes are uniformly distributed between 40 minutes and 65 minutes.
- What is the probability that a randomly selected cable repair visit will take at least50 minutes?
- What is the probability that a randomly selected cable repair visit will take at most55 minutes?
- What is the expected length of the repair visit?
- What is the standard deviation?

- In a certain study, it is found that the life of a light bulb is exponentially distributed witha mean life of 1,200 hours.
- What is the probability that a randomly selected bulb will last more than 1,400 hours?
- What is the probability that the bulb will last less than 1,000 hours?
- What is the median life of a bulb?

- A professor grades his students on a normal distribution with a mean score of 70 and astandard deviation of 10. If there are 125 students in his class, about how many scores are between 75 and 85?
- Suppose that the waiting time for a pizza to be delivered to an individual’s residencehas been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time:
- Between 15 and 45 minutes?
- At least 10 minutes?
- No more than 22 minutes?

- In an exam, an instructor plans to give those students in the top 5% an A. If the average score on this exam is 75 with a standard deviation of 8, then what would be the minimum score for an A? Assume normality for the distribution of scores.
- It has been reported that the average time to download the home page from a governmentwebsite was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected:
- Describe the shape of the sampling distribution. How was this determined?
- Calculate the mean of the sampling distribution of the sample mean.
- Calculate the standard deviation of the sampling distribution of the sample mean.
- 80% of the sample means will be between what two values that are symmetrically distributed around the population mean?
- What is the probability that the sample mean will be less than 0.80 seconds?

**MINITAB question: Normal approximation to binomial**- Use MINITAB to find cumulative probabilities
*P*(*X*≤*x*) for a binomial distribution with parameters*n*= 30 and*p*= 0*.*Show your MINITAB output.

- Use MINITAB to find cumulative probabilities

- During off hours, cars arrive at a highway service station at an average rate of 5 cars per10 minutes. The number of cars arriving at the service station is distributed according to a Poisson distribution.

To find the cumulative probabilities, follow the sequence:

In column c1, put values of x;

Choose **Calc ***> ***Probability Distributions ***> ***Binomial**; Specify the parameters in the box; Put c1 in Input column.

- Compute the probability
*P*(4 ≤*X*≤ 8) using the MINITAB output. - Use the normal approximation to the binomial distribution to calculate the probability
*P*(4 ≤*X*≤ 8) by hand. How does this probability compare to that in part (b)?

**MINITAB question: Normal distribution**. Generate a random sample of 200 observations from a normal distribution with mean 5 and standard deviation 2 and store the data in column c2.

To generate the data, follow the sequence:

**Calc ***> ***Random Data ***> ***Normal**;

Input 200 in Generate window; Put c2 in Store In Column(s) window;

5 for mean and 2 for standard deviation.

- Draw a histogram of these data. Comment on the shape of the distribution.
- Using MINITAB, calculate the sample mean ¯
*x*and the sample standard deviation*s*of the 200 observations in c2. Are these values what you expected them to be? Explain.

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