Targeted Review Solutions

For problems 1–4, use the table.

An observational study was conducted with 152 people. Observers recorded each person’s dominant hand and teeth-brushing hand.

		Teeth-Brushing Hand
		Right	Left
Dominant Hand	Right	85%	4%
Dominant Hand	Left	2%	9%

Determine the number of people who are left-handed and brush their teeth with their right hand.

$2 % of 152 (0.02) (152) = 3.04$

3 people

Determine the percentage of people who are left-handed and also brush their teeth left-handed.

Use the two-way table.

If a person is selected randomly, how likely is it that they will use their right hand to brush their teeth?

$85 % + 2 % = 87 %$

It is very likely (87%) that a randomly selected person will brush their teeth with their right hand.

Note

The number line from the warmup can be helpful to describe likelihood.

Determine the number of people who use their dominant hand to brush their teeth.

$85 % + 9 % = 94 % 94 % of 152 (0.94) (152) = 142.88$

143 people

Expand: ${(2 x - 1)}^{5}$

$1, 5, 10, 10, 5, 1 1 {(2 x)}^{5} + 5 {(2 x)}^{4} (- 1) + 10 {(2 x)}^{3} {(- 1)}^{2} + 10 {(2 x)}^{2} {(- 1)}^{3} + 5 (2 x) {(- 1)}^{4} + 1 {(- 1)}^{5} 32 x^{5} + 5 (16 x^{4}) (- 1) + 10 (8 x^{3}) (1) + 10 (4 x^{2}) (- 1) + 5 (2 x) (1) + (- 1)$

$32 x^{5} - 80 x^{4} + 80 x^{3} - 40 x^{2} + 10 x - 1$

Charlotte has 5 shirts, 6 pairs of jeans, and 4 pairs of shoes. How many different outfits can she put together?

$5 \cdot 6 \cdot 4$

Charlotte can create 120 outfits.

A television network wants to estimate the average number of minutes a household watches a particular prime-time news program. The network requires the estimate to be within 5 minutes of the true average viewing time. If a 99% confidence interval is used, what is the minimum sample size that can be taken using a standard deviation of 22.5 minutes?

$\begin{matrix} E = 5 & E = z \cdot \frac{s}{\sqrt{n}} \\ z = 2.576 & 5 = (2.576) (\frac{22.5}{\sqrt{n}}) \\ s = 22.5 & \frac{5}{2.576} = \frac{22.5}{\sqrt{n}} \\ 5 \sqrt{n} = 2.576 \cdot 22.5 \\ {(\sqrt{n})}^{2} = {(\frac{2.576 \cdot 22.5}{5})}^{2} \\ n = 134.37 \end{matrix}$

The television network needs to survey at least 135 households to be 99% confident in the average number of minutes a news program is watched.

What is the z-score of the observed difference?

The z-score of the observed difference is the difference of the means (treatment and control) divided by the simulated standard deviation.

Multiple Choice

Emil has a bag containing two red dice, ten blue dice, and four white dice. If Emil selects a single die from the bag without looking, what is the chance of selecting white?

1 out of 8
1 out of 4
5 out of 8
3 out of 4

$Total : 2 + 10 + 4 = 16 P (white) = \frac{4}{16} = \frac{1}{4}$

Note

This option is the probability of selecting red.
This option is the probability of selecting blue.
This option is the probability of selecting red and blue.

The probability of a baby being born with blue eyes when both parents have brown eyes is around 25%. What is the probability that the baby will not have blue eyes?

0%
75%
25%
100%

$1 - 0.25 = 0.75 = 75 %$

Note

0% is an impossible event.
This option is the probability.
100% is a certain event.

Select the question that is unbiased.

Would your ride to work be more enjoyable if the traffic were less horrendous?
Does it really take that long to drive to work?
How long was your drive to work today?
If your job actually makes you drive to the office, how long does it take?
1. Bias: more enjoyable, less horrendous
2. Bias: really take that long
3. Bias: actually makes you drive

Note

A, B, D) All of these options include biased wording.

New equipment for physical therapy was introduced at one of eight office locations. The therapist saw that patients recovered 3.2 weeks faster ( $z = 2.32$ ), but the cost of the equipment was $17,500. What should be considered when deciding if all eight offices will update their equipment?

Only the cost should be considered.
Only the statistical significance should be considered.
Both the statistical significance and the cost should be considered.
No considerations are needed when the results are statistically significant.

A z-score greater than 1.96 is statistically significant.

Note

This option ignores significant patient improvement.

B, D) These options ignore the cost of the equipment, and if all offices can afford it.

Problem	1	2	3	4	5	6	7	8	9	10	11	12
Origin	L54	L54	L54	L54	L52	L51	L49	L50	L53	L53	L48	L50

L = Lesson in this level, A1 = Algebra 1: Principles of Secondary Mathematics