STAT QUIZ SOLUTION

QUESTION 1

1. Car wash waiting times at the local convenience store follow a uniform distribution.  The wait time ranges from 0-16 minutes.  What is the mean waiting time at the car wash?

10 points   

QUESTION 2

1. The mean of a normal distribution of a set of truck tires is 300 pounds with a standard deviation of 10 pounds.  What is the probability of a randomly selected set of tires weighing between 300 and 330 pounds?

10 points   

QUESTION 3

1. A study of customer service phone calls indicates the calls average 20 minutes.  The standard deviation equaled 5 minutes.  Assuming that the distribution is normal, what percent of the calls took longer than 10 minutes to complete?

10 points   

QUESTION 4

1. The mileage of transatlantic flights is normally distributed with a mean of 1000 miles and a standard deviation of 50 miles.  What is the probability of a randomly chosen flight being 850 miles or less?

10 points   

QUESTION 5

1. The mean cost of a Ranger fishing boat is $30,000.  Assume the boat purchase cost follows a normal distribution and the standard deviation is $5,000.  Ninety percent of all Ranger boat buyers pay less than what amount?

10 points   

QUESTION 6

1. According to an IRS study, it takes 300 minutes for tax payers to prepare, copy, and electronically file a 1040A tax return.  The distribution of completion times follows a normal distribution and the standard deviation is 25 minutes.  What is the likelihood the sample mean is between 290 and 325 minutes?

10 points   

QUESTION 7

1. Competition shooters were divided by accuracy.  The students were divided into categories, above 90% accuracy, between 80% and up to 90% accuracy, and between 70% and up to 80% accuracy.  Shooters were surveyed from each of these groups and then asked about the type of ammunition used.  What type of sampling scheme is this?

10 points   

QUESTION 8

1. UCA admissions completed a survey of students.  First, the state where students resided in high school was subdivided into zip codes.  Five zip codes are selected at random and further sampling was concentrated in these five zip codes.  What type of sampling method/technique is this?

10 points   

QUESTION 9

1. A telephone surveyor is interviewing individuals about the upcoming elections. A random starting point is chosen in the phone book and every tenth person in the phone book is asked which of the three candidates they would vote for.  What type of sampling method/technique is this?

10 points   

QUESTION 10

1. A human resources manager is concerned about the ease of use of the employee website.  She decides to use a random number generator to select 10% of the workforce by the last four of their social security number for a survey that asks questions concerning the website.  What type of sampling scheme is this?

10 points   

QUESTION 11

1. The Central Limit Theorem states that if the sample size "n" is sufficiently small, the sampling distribution of the sample means will be approximately normal, even when the population itself is skewed or uniform.

10 points   

QUESTION 12

1. 64 samples were taken of a stream flow over the course of a year. A sample mean of 16 cubic feet per minute (cfm) was calculated.  The population standard deviation of stream flows is 2 cfm.  Calculate the 90% confidence limits (LCL, UCL).

10 points   

QUESTION 13

1. 49 samples were taken of a stream flow over the course of a year.  A sample mean of 16 cubic feet per minute (cfm) was calculated.  The sample standard deviation of stream flows is 2 cfm as no population standard deviation was available. What are the 95% confidence limits?

10 points   

QUESTION 14

1. We wish to estimate the population mean weight of wooden trusses at the lumber mill within 5 pounds, with a 95% level of confidence.  The population standard deviation is estimated to be 30 pounds.  How many samples do we need to collect to make an accurate estimation?

10 points   

QUESTION 15

1. The t distribution is used when the population standard deviation is unknown.   If you sample 33 fisherman concerning their favorite type of lure for largemouth bass.  What is the value of "t" you would use in any further calculations if you wanted 99% confidence?  If you knew the population standard deviation for fishermen in this case, what is the value of z you would use in any further calculations for 99% confidence?

10 points   

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