Lesson 2 Just ACT Normal Solidify Understanding

Ready

1.

You and your friend are rolling one die over and over again. After $6 rolls$ , your friend has rolled four fives. Are you surprised by these results? Explain.

2.

After rolling the die $50 times$ , you notice that you rolled a total of $20$ fives. Are you surprised now? Explain.

3.

You survey $100 people$ in your school and ask them if they feel your school has adequate parking. Only $30 %$ of the sample feels the school has enough parking. If you have $728 students$ total in your school, how many would you expect out of all the student body to feel there is enough parking?

Set

4.

The population of NBA players is normally distributed with a mean of $6^{'} 7^{''}$ and a standard deviation of $3.9 inches$ . (Wikipedia) Greg is considered unusually tall for his high school at $6^{'} 3^{''}$ .

a.

What percent of NBA players are taller than Greg?

b.

What percent are shorter?

c.

How tall would Greg have to be in order to be in the top $2.5 %$ of NBA player heights?

5.

The average height of boys at Greg’s school is $5^{'} 9^{''}$ with a standard deviation of $2^{''}$ . We will assume the population is normally distributed.

a.

What percent of students in the school are shorter than Greg?

b.

What percent of students are between $5^{'} 5^{''}$ and $5^{'} 11^{''}$ ?

6.

Jordan is drinking a cup of hot chocolate. From previous research, he knows that it takes an average time of $10 minutes$ for the hot chocolate to reach a temperature where his tongue will not burn. The time it takes the chocolate to cool varies normally with a standard deviation of $2 minutes$ .

a.

How long should he wait to drink his hot chocolate if he wants to be $84 %$ sure that he won’t burn himself?

b.

If he waits $8 minutes$ , what percent of the time will he burn his tongue?

Go

Use the properties of logarithms to expand the expression as a sum or difference and/or constant multiple of logarithms. (Assume all variables are positive.)

7.

$f (x) = \log_{2} 3 x$

8.

$f (x) = \log_{x} \frac{5}{7}$

9.

$f (x) = \ln \sqrt[3]{x}$

10.

$f (x) = \log \frac{2 x^{2} y^{4}}{3 z^{2}}$

11.

$f (x) = \log_{3} \frac{16 x^{2} - 36}{x^{2}}$

12.

$f (x) = \log \frac{x^{2} + 12 x + 20}{5}$

13.

$f (x) = \log_{3} 27 x^{7}$

14.

$f (x) = \log 10^{5} \sqrt{y}$