ECON1193 Business Statistics Week 3

Which of the following are examples of continuous variables? More than one option can be selected

• Your parents' age

• The distance from your house to RMIT

• Your bank account balance

• The number of pets one can have

• Your weight or height

A normal distribution has a ... shape and describes the tendency of data clustering around a central value, which is the ...

• bell, population mean

• bell, sample mean

• circle, populations standard deviation

• bell, sample standard deviation

Which of the following are characteristics of a normal distribution? Select all the correct answers

• Bell-shaped

• Asymmetrical

• Mean = Median = Mode

• Data value center at the sample mean

• Spread is determined by the sample standard deviation

Which statement is correct when describing a standardized normal distribution?

• A standardized normal distribution is known as z-distribution, which has a mean of  $\mu$  and a standard deviation of  $\sigma$  

• A standardized normal distribution is known as t-distribution, which has a mean of 0 and a standard deviation of 1. 

• Values above the mean have positive z-values and values below the mean have negative z-values.

• None of the above

If Assignment 1 mark is normally distributed with a mean of 60 and a standard deviation of 20, the z-value for a student who gets 85 for his/her assignment:

• Z = 1

• Z = -2

• Z = 1.25

• Z = -1.5

• Z = 0

The total area under the normal distribution curve is

• 1

• 100%

• 0.5

• 0

• Either one of the first two options is correct

Please choose the correct distribution rules of a normal distribution:

• $\mu\pm2\sigma\approx68.26\%$
  

• $\mu\pm\sigma\approx95\%$

• $\mu\pm2\sigma\approx95\%$

• $\mu\pm3\sigma\approx99.73\%$

Suppose X is normally distributed with a mean of 12 and a standard deviation of 3.0. Find P(X > 10)

• 0.74751

• 0.25249

• 0.24751

• 0.53684

• 0.47359

Suppose the income per capita in Vietnam is a normal distribution with a mean of $250 and a standard deviation of $300. P(200 < X < 600) is closest to.

• 0.56247

• 0.44453

• 0.33676

• 0.65561

• 0.24225

Which of the following statements is correct?

• The population mean characterizes the spread of the normal distribution

• The population mean characterizes the position of the normal distribution

• The population standard deviation characterizes the position of the normal distribution

• A normal distribution is asymmetrical around the population mean