6.8 Normal distribution: review

Explain which of the following are false and which are true.

• a $f(x)=\frac{1}{\text{10}}$ ,
• b There is no mode.
• c The median is less than the mean.
• d

Calculate:

• a Mean
• b Median
• c 65th percentile.

Which of the following is true for the above box plot?

• a 25% of the data are at most 5.
• b There is about the same amount of data from 4 – 5 as there is from 5 – 7.
• c There are no data values of 3.
• d 50% of the data are 4.

If $P(G\mid H)=P(G)$ , then which of the following is correct?

• A $G$ and $H$ are mutually exclusive events.
• B $P(G)=P(H)$
• C Knowing that $H$ has occurred will affect the chance that $G$ will happen.
• D $G$ and $H$ are independent events.

If $P(J)=0\text{.}3$ , $P(K)=0\text{.}6$ , and $J$ and $K$ are independent events, then explain which are correct and which are incorrect.

• A $P\left(J\mathrm{and}K\right)$ $=0$
• B $P\left(J\mathrm{or}K\right)=0.9$
• C $P\left(J\mathrm{or}K\right)=0.72$
• D $P\left(J\right)\ne P(J\mid K)$

On average, 5 students from each high school class get full scholarships to 4-year colleges. Assume that most high school classes have about 500 students.

$X$ = the number of students from a high school class that get full scholarships to 4-year school. Which of the following is the distribution of $X$ ?

• A P(5)
• B B(500,5)
• C Exp(1/5)
• D N(5, (0.01)(0.99)/500)