Probability and distributions

What is Probability?

• A number >1

• A number >0 but <1

• A %

• A Negative Odd

Answer explanation

$Right\ \ \ a\ \ \ \ \ \ \ \ \ \ 0\ <P\left(x\right)\ <1$

Which one of the following is a discrete random variable?

• Sam's height

• Sam weight

• Time Sam's runs the 110 m hurdles

• Amount of Sam's brothers and sisters

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

Is the number of days, W, in a given week a discrete random variable?

• Yes

• No

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.

• Yes
• No, the trials are not independent.
• No, there are more than 2 outcomes

A stockbroker estimates that at the end of the year, there is a 40% chance a stock will be worth $50, a 35% chance it will be worth $60 and a 25% chance it will be worth $70.
What expected value does this broker assign to this stock's end-of-the-year price?

• $58.50
• $60.00
• $62.50
• $65.00

Find the missing value for P(X=5) in the probability ditribution:

Number of Toys | Probability

0| 0.03

1| 0.16

2| 0.30

3| 0.23

4| 0.17

5| ?

• 0.11

• 0.21

• 0.01

• 0.31

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

The table above shows a television station's advertisement sales. The distribution of sales for one 24-hour day is given. Solve for the mean. Round to the nearest hundredth.

• 31.8

• 15.68

• 0.20

• 1.00

Find the mean of a binomial distribution with n=50 and p=0.4

• 50

• 4

• 20

• 10