07 Jan What are the primary

Week 3 discussion

MAT2058 Discussion Questions

Week 3

Text:

Textbook: Triola, M. F. (2014). Elementary statistics technology update (12th ed.). Boston, MA:

Pearson Education.

Instructions:

• In the Course Home announcement area there should be a listing with your name and letter assigned for the discussion questions. If there is not such a list, then find the first letter of your last name below, and complete the two discussion associated with this letter.

• Please show all of the steps and processes you used to solve each of the problems.

• Remember to do both of the problems assigned and to respond to two of your classmates’ solutions.

• Please try to respond to two of your classmates who have had very different problems than yours assigned to them. You should receive more credit for doing so.

• In responding to the postings of at least two of your classmates, you can

o ask a question about your classmate’s solution(s)

o offer help when you see an error, or

o seek help in completing your own problems.

Remember that non-substantive posts such as “Good job!” will not count toward your participation score. Again, try to respond to at least two classmates who have problems assigned that are quite different from yours.

Please note that the assigned problems vary in difficulty and the list has been randomly generated for each of the two assigned problems.

Revised Week 3 Discussion Questions

See the first instruction

on the previous page.

Please submit the two discussion items for your assigned letter.

Examine the intelligence quotient, or IQ, as it

is defined by the formula:

Assuming a normal distribution, what is the z-score “intelligence quotient = 100 * (mental

A associated with the 90th percentile? &

age/chronological age)”

What would be the IQ if a person’s

chronological age equals their mental age?

&

What percentage of the area would the Empirical

B Rule say is between z = -3.00 and z = +3.00? Given x = 237, ? = 220, and ? = 12.3, find z.

In looking at the properties of the Standard &

Normal Distribution below:

Properties of the Standard Normal Distribution:

1. The total area under the normal curve is

equal to 1.

2. The distribution is mounded and Given that x is a normally distributed random

symmetrical; it extends indefinitely in both

variable with a mean of 28 and a standard

directions, approaching but never touching the

deviation of 7, find the following probability:

horizontal axis.

C

P(x < 28) = P(z< ?) = ? 3. The distribution has a mean of 0 and a standard deviation of 1. 4. The mean divides the area in half—0.50 on each side. 5. Nearly all the area is between z = ?3.00 and z = 3.00. Which of these properties does not necessarily apply to any normal distribution? & How would standard (z) scores of -2.00 and +2.00 be Find the z-score for the standard normal D interpreted using the Standard Normal Distribution distribution where: Table (A-2) in the text? P(z < +a) = 0.8980 E What one characteristic about the Standard Normal & Distribution make it different from any normal Find the z-score for the standard normal distribution? distribution where: P(z < -a) = 0.0721 Find the standard z-score that corresponds to What are the primary advantages of the Standard the following: F Normal Distribution that other normal distributions & Eighty percent of the distribution is below (to do not have? the left of) this value. If the random variable z is the standard normal score Find the (two) z-scores that bound the middle G and a > 0, is it true that P(z > -a) = P(z < a)? Why or & 40% of the standard normal distribution. why not? If n = 100 and p = 0.02 in a binomial experiment, Find the z-score for the standard normal H does this satisfy the rule for a normal approximation? & distribution where: Why or why not? P(z< -a) = 0.2451 If n = 100 and p = 0.05 in a binomial experiment, Find the z-score for the standard normal does this satisfy the rule for a normal approximation? distribution where: I Why or why not? & P(z 0, is it true that P(z < -a) = P(z > a)? Why or & distribution where:

why not? Area = 0.32 in the left tail

P Suppose that x has a binomial distribution with n = & Find the z-score for the standard normal

15 and p = 0.3. Is the normal approximation distribution where:

reasonable for this binomial distribution? P(-a 2.43)

S Assuming a normal distribution, what is the z-score & Find the following:

associated with the second quartile? P(z < ?0.43) Find the probability that a data value picked at Give an example of when and why one would use a random from a normally distributed population will have a standard score that T continuity correction factor? & corresponds to the following: Less than 3.00 If the random variable z is a Standard Normal Score, Find the area under the standard normal curve what is P(-1.00 ? z ? +1.00)? How did you find this U & to the left of z = ?1.53. This may also be probability? stated as P(z < ?1.53). V Use the standard normal table to find P(z ? 0.15) & Find the area under the standard normal curve to the left of z = 1.73. This may also be stated as P(z < 1.73). Find the probability that a data value picked at Use the standard normal (z score) table to find: random from a normal population will have a standard score (z) that lies between the W P(-1.00 ? z) & following pairs of z-values. z = 0 to z = 2.10 Find the area of the standard normal distribution is For the problem that you worked to the left, between z = -1.00 and z = +1.00 using both the X & what is the percentile rank of the value z = Empirical Rule and the Standard Normal Table in the +1.00? appendix of the text.. Use the standard normal table to find P(-1.50 ? z ? Find the area under the standard normal curve Y & between z = 0 and z = 1.37. 0.00) One definition of IQ is the Binet Intelligence What are the primary differences between a “normal Scale, whose mean is 100 and standard deviation is 16. distribution” and a “standard normal distribution”? Z & What percentage of the population would Why would one want to use one over the other? most likely have IQ scores between 68 and 132 according to this scale?