Homework answers / question archive / 1) Which ones of the following are continuous random variables? (Note: you have to tick all correct options) Select one or more: a

1) Which ones of the following are continuous random variables? (Note: you have to tick all correct options) Select one or more: a

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1) Which ones of the following are continuous random variables? (Note: you have to tick all correct options)

Select one or more:

a. Number of customers who like the product

b. The weight of a shipment of goods

c. The salary of a fresh graduate

d. The time a customer spent queuing before being served

e. Number of cars arriving at tollbooth

f. Number of customers who are 45 year old and older

2 Suppose the average mark of a statistic course is normally distributed with a mean of 27 and a standard deviation of 7.3. 

If a student receive a mark of 3.2, calculate the z-score.

Answer: ?

3 P(Z < - 1.25) = 

Select one:

a. 0.691

b. 0.106

c. 0.841

d. 0.159

e. 0.023

4 What is the 97.7th percentile of a z distribution?

Hint: Find b, such that P(Z < b) = 0.977

Answer: ?

5 Exam grades across all sections of introductory statistics at a large university are approximately normally distributed with a mean of 72 and a standard deviation of 11. Use the normal distribution to answer the following questions.

Approximately, what percent of students scored below a 90?

Select one:

a. 95%

b. 5%

c. 14%

d. 86%

6 Writing portion of the SAT (Scholastic Aptitude Test) exam are normally distributed with mean 492 and standard deviation 111. Use the normal distribution to answer the following questions:

What is the estimated percentile for a student who scores 452 on Writing?

Select one:

a. 64th percentile

b. 42nd percentile

c. 58th percentile

d. 36th percentile

e. 20th percentile

7 In a random sample of 100 people in Parramatta, only 60 said "Regularly buy items from Coles". Provide an expression for 95% confidence interval for the proportion of Parramatta people who shops at Coles regularly.

Select one:

a. 0.6 ? 1.96

b. 0.6 ? 1.96*√(1/100)

c. 0.6 ? 1.645*√((0.6*0.4)/100)

d. 0.6 ? 1.96*√((0.6*0.4)/100)

8 A random sample of 30 households was selected as part of study on electricity usage, and number of kilowatt per hours(KWH) was recorded. The average usage was found to be 375 KWH.Census was conducted for same purpose last year and it was found that the standard deviation of the usage was 81 KWH. Assuming the standard deviation is unchanged and that usage is normally distributed, provide an expression for a 99% confidence interval for the mean usage.

Select one:

a. 375 ? 2.575 * 9/√30

b. 375 ? 2.330 * 81/√30

c. 375 ? 2.752 * 81/√30

d. 375 ? 2.575 * 81/√30

9 The price of a brand jeans in a sample of 16 retailers is on average $141 with a standard deviation of 4. If this is a random sample and the prices can be assumed to be normally distributed, which of the following gives an expression for an 95% confidence interval for the average price:

Select one:

a. $141 ± 2.120

b. $141 ± 1.753

c. $141 ± 1.960

d. $141 ± 2.131

10 A 95% confidence interval for the mean number of televisions per Australian house hold is between 1.15 and 4.20.

Which of the following statement is the correct interpretation of the confidence interval given above.

Select one:

a. We are 95% confident that the true mean number of television per Australian household is between 1.15 and 4.20

b. 95% of the samples should have its sample mean.

c. 95% of the Australian household have between 1.15 and 4.20 televisions.

d. The probability that μ is between 1.15 and 4.20 is 0.95.

11 A survey on a random sample of 400 full-time employees in Australia gave an average weekly salary of $1539 with a standard deviation of 201.

Construct a 95% confidence interval for full-time weekly salary in Australia and write down the lower limit of the interval (up to 3 decimal places).

Hint: the upper limit is 1558.698

Answer: ?

12 A random sample of 500 males was asked if they would prefer to have a job outside the home or if they would prefer to stay at home to care for the family and home. 325 said they would prefer to have a job outside of the home. 

Construct a 95% confidence interval for the proportion of males who would prefer to have a job outside of the home and write the upper limit of the interval (up to 4 decimal places).

Hints: The lower limit is 0.6081917711449

Answer: ?