Lesson 3 Y B Normal? Solidify Understanding

Ready

The enrollment at South Beach High School is $2,500 students$ . Mariana surveyed $40$ of her friends regarding where they prefer to eat lunch. She created the following two-way table showing her results.

	9th Grade	10th Grade	11th Grade	12th Grade	Totals
School Cafeteria	$18$	$6$	$2$	$1$	$28$
Off Campus	$2$	$4$	$3$	$4$	$12$
Totals	$20$	$10$	$5$	$5$	$40$

Mariana plans to use her data to answer the following questions:

Do students prefer to eat on campus or off campus?
Is there a difference between grade levels for where students prefer to eat lunch?

1.

In Mariana’s sample, what percent of students prefer school lunch?

2.

What percent prefer to eat off campus?

3.

a.

For each grade level in her sample, determine the percent of students who prefer school lunch and the percent who prefer off-campus lunch.

	9th Grade	10th Grade	11th Grade	12th Grade
Prefer School Lunch
Prefer Off Campus

b.

Do you notice anything unusual?

4.

Based on her sample, Mariana concludes that students at South Beach High School overall like school lunch. Do you agree or disagree? Why?

Set

A company generates a mean monthly revenue of $$20,300$ with a standard deviation of $$3,200$ . In one given month, the company makes $$29,500$ .

5.

Find the $z$ -score.

6.

Assuming the company’s monthly revenue is normally distributed, what percent of the time does the company make more than this amount? Less than?

7.

What percent of the time does the company make between $$15,000$ and $$25,000$ ?

8.

If the company needs to make $$16,400$ in order to break even, how likely in a given month is the company to make a profit?

On the Wechsler Adult Intelligence Scale, an average IQ is $100$ with a standard deviation of $15 units$ . (Source: https://openup.org/DcTE5Z)

9.

IQ scores between $90$ and $109$ are considered average. Assuming IQ scores follow a normal distribution, what percent of people are considered average?

10.

One measure of genius is an IQ score above $135$ . What percent of people are considered genius?

11.

Einstein had an IQ score of $160$ . What is his $z$ -score?

12.

What is the probability of an individual having a higher IQ than Einstein?

Go

Without using technology, sketch the graph of the polynomial function with the given characteristics. Write the equation, if it’s not given.

13.

Degree: $4$

Roots: $- 1$ multiplicity $2$ , $5$ , $- 2$

$y$ -intercept: $20$

Equation:

14.

$f (x) = (x + 2) {(x - 3)}^{3}$

15.

$g (x) = - x {(x - 3)}^{2} (x + 5) (x - 5)$

16.

Degree: $3$

$f (- 1) = 10$

$f (2 i) = 0$

$f (3) = 0$

Equation: