Use the information given below to answer questions 1. to 4.
Suppose you are a budding entrepreneur. The start-up costs, in thousands of dollars, for Entrepreneur Magazine's 25 most popular franchises are summarised below.
1. The franchise Hardees has the highest start-up costs. What is the approximate start-up cost for a Hardees restaurant?
A. $660
B. $600
C. $300 000
D. $660 000
E. $600 000
2. The shape of this distribution of start-up costs is
A. approximately normal.
B. positively skewed.
C. negatively skewed.
D. uniform.
E. skewed to the left.
3. It was reported that for these 25 franchises, the typical start-up cost was $160 700. Which measure of centre is this value most likely to represent?
A. mean
B. median
C. mode
D. the 50th percentile
E. standard deviation
4. What does the value marked with an arrow on the boxplot correspond to?
A. the 75th percentile
B. the largest observation
C. an outlier
D. the 25th percentile
E. the largest value that is not considered a potential outlier
5. The mean and standard deviation for the following sample of 10 numbers
12 15 20 14 15 12 20 19 26 29
A. are 18.2 and 5.47 respectively.
B. are 18.2 and 29.96 respectively.
C. are 18.2 and 5.77 respectively.
D. are 18.2 and 33.29 respectively.
E. are none of the above values.
6. A simple random sample of size 8 is selected from a population of 40. The probability that a particular member is the first one selected is
A. 0.025
B. 0.125
C. 0.2
D. 0
E. none of the above
7. Two events A and B are independent. If P(A) = 0.5 and P(B) = 0.3 then P(B|A) is
A. 0.15
B. 0.30
C. 0.67
D. 0.50
E. unable to be determined due to insufficient information.
8. Which of the following is an example of a continuous random variable?
A. The weight of a packet of lollies.
B. The number of lollies in a bag.
C. The number of phone calls received by a switchboard in an hour.
D. The number of workers absent today.
E. The number of questions answered correctly on a multiple choice test.
9. A market researcher is asked to visit 15 homes in a given area between 7:30 and 9:30 one evening. Previous calls suggest that there will be someone at home in 90% of homes. Find the probability that the researcher will find someone at home in exactly ten homes.
A. 0.013
B. 0.011
C. 0.987
D. 0.056
E. 0.349
10. A test has been conducted to see if a road intersection should be improved. During this test it was found that cars arrive randomly and independently at the intersection at an average rate of 15 cars every half an hour. What is the probability that more than five cars will arrive during a ten minute period?
A. 0.560
B. 0.997
C. 0.762
D. 0.616
E. 0.384
11. Given Z is the standard normal random variable, find the probability that P(1.5 < Z < 2.5)
A. 0.9270
B. 0.0606
C. 0.9394
D. 0.9938
E. 0.1267
Use the following information to answer questions 12. and 13.
A fast-food restaurant finds that the number of meals that it serves in a week is normally distributed with a mean of 6000 and a standard deviation of 600 meals.
12. What is the probability that in a given week the number of meals served will be less than 5000?
A. 0.0475
B. 0.4525
C. 0.5475
D. 0.0485
E. 0.4515
13. There is a 90% chance that the number of meals served in the restaurant will exceed
A. 6768
B. 5850
C. 5940
D. 5232
E. 5226
14. The standard error for the sample mean gives a measure of
A. the dispersion of values in the sample.
B. the dispersion of values in the population.
C. how far away a particular sample mean is from the population mean.
D. the dispersion of the values of the sample mean for all possible samples.
E. the variability of the data.
15. A machine is set to produce bolts with a mean length of 3.5cm. A quality control inspector takes a random sample of 50 bolts and calculates a mean bolt length of 3.7cm and a standard deviation of 0.8cm. Find the probability of getting a sample mean that size or larger if the machine is set correctly.
A. 0.4616
B. 0.0987
C. 0.4013
D. 0.0384
E. 0.9616
16. Timball Corporation employs 5600 workers. 60% of the workers are male. 25% of the workers earn more than $30 000 a year. 15% of the workers are male and earn more than $30 000 per year. If an employee earns more than $30 000 a year, what is the probability that the employee is female?
A. 0.15
B. 0.45
C. 0.10
D. 0.30
E. 0.40
17. A sample of 24 observations is taken from a large population. The sampling distribution of the sample mean is
A. approximately normal because the sample means are always normally distributed.
B. approximately normal because the sample size is large.
C. approximately normal because the sample size is small.
D. approximately normal because of the central limit theorem..
E. normal if the population is normally distributed.
18. For a continuous uniform distribution with limits of 10 and 20, the range defined by one standard deviation either side of the mean is
A. 12.11 to 17.89
B. 5.77 to 11.55
C. 4.22 to 25.78
D. 9.22 to 20.78
E. 6.67 to 23.33
19. The reason why the standard deviation of a distribution is more easily interpreted than the variance is that
A. it is a measure of average deviation.
B. it is expressed in the same units as the data.
C. it takes into account every data value.
D. it is standardised
E. it takes the mean into account.
20. A bag contains 1 yellow and four red balls. A ball is drawn at random from the bag and the colour recorded. The ball is then replaced and the bag shaken. This is repeated three times more. How likely is it that we observe 4 yellow balls?
A. 0.8
B. 0.2
C. 0.16
D. 0.64
E. 0.0016