## Question

a) What is the area under the standard normal curve to the left of z = 0.89? (4dp)

b) What is the area under the standard normal curve between z = -0.89 and z = 1.63? (4dp)

c) What is the z-value that gives the right hand tail area equal to 0.0268? (2dp)

d) What is the absolute value of z such that the total area under the standard normal curve between -z and +z will be 0.9443? (2dp)

Q2 The daily exchange rates for the two-year period 2011 to 2013 between the Japanese Yen (JPY) and the Australian Dollar (AUD) can be modelled by a Normal distribution with mean, p = 83 Yen and a standard deviation, CJ= 22 Yen.

use Excel to help you solve the following problems.

1. What is the probability that on a randomly selected day during this period, the dollar was worth less than 69 Yen? (4 dp)

2. What proportion of the days during this period will the dollar be worth between 69 and 98 Yen? ( 4 dp)

3. If you select a window of 250 days during this period, how many days would you expect the dollar to worth between 69 and 98 Yen?(round to nearest integer)

Q3 A company's Human Resources department administers a test of "Executive Aptitude". Test scores are known to be normally distributed with a mean of 100 and a standard deviation of 15.

1. What score do you need to be in the top 12% of the applicant pool? (integer)

2. What is the score at the 55th percentile? (integer)

Q4) An important step in creating confidence intervals for proportions is to check whether the success/failure conditions have been met otherwise the interval created will not be valid (i.e. we should not have created that interval).

The following examples are estimating the proportion of people in the population who exercise regularly. Try to determine whether or not the assumptions have been met.

a) In a sample of 45 people surveyed, 43 exercised regularly.

b) In a sample of 24 people surveyed, 18 exercised regularly.

c) In a sample of 12 people surveyed, 8 exercised regularly.

d) In a sample of 105 people surveyed, 47 exercised regularly.

Q5) The human resources department of a very large organisation is trying to determine the proportion of all employees that are satisfied with their current position. They randomly select 100 employees and ask them: "Are you satisfied with your current position?" 67 replied yes they were. Construct a 95% confidence interval to estimate the true proportion of all employees at this workplace who were satisfied with their position.

A 95% confidence interval for the true proportion of all employees at this workplace who were satisfied with their position is between (round your answers to 2 dp)

_____ and _______

Q6 A researcher surveyed a random sample of 40 people who had been given the flu vaccine in 2017 and found that 26 did not contract the flu that year. A 95% confidence interval for the proportion of all people who have been vaccinated and did not contract the flu is between 0.502 and 0.798. Using the confidence interval can we make the following statement? The flu vaccine is effective (i.e. it prevents the flu) in 50% of those vaccinated.

Which is true?

a) Yes that statement is correct.

b) No it was effective in less than 50% of those vaccinated.

c) No it was effective in more than 50% of those vaccinated.

## Solution Preview

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Q1(a) 0.8133(b) 0.7617

(c) 1.9...

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