Hello, Chegg! I was wondering if anyone would be able to help me with this assig

Question

Hello, Chegg! I was wondering if anyone would be able to help me with this assignment. I know it's a little over 6 parts, but I really appreciate it!

A. A ship has 9 different signal flags available. To form a signal, 3 flags are flown one above another along a vertical pole. How many different signals can be made?

B. Kyra has missed several of her biology classes and has not even read the material for the days she missed. She has just received a 10-question True/False quiz. What is the probability that she got all of them right?

C. In the Illinois Lottery game Little Lotto, 5 balls are drawn without replacement from an urn containing balls numbered 1-30. To win, all 5 of the numbers on a player's ticket must match all 5 of the numbers drawn from the urn. Note that the order in which the balls are selected does not matter. What is the probability of a ticket holding the winning numbers?

D. On a television game show, a contestant is shown a set of 5 prizes and a set of 5 price tags. If he matches all of the price tags to their correct prizes, then he wins all of the prizes; otherwise, he wins nothing. What is the probability that he wins by placing the price tags with the prizes completely at random?

• In his article, "American Football" (published in Statistics in Sports ), Iowa State University statistician, Hal Stern, evaluates winning strategies of teams in the NFL. In a section on estimating the probability of winning a game, associated with certain outcomes (i.e. running play, short pass plays, long pass plays). The following table gives the probability distribution for the yardage gained, X, on a running play. Note that a negative gain represents a loss of yards on the play.

E. Verify that X has a well-defined probability distribution.

F. Find the probability of gaining 10 yards or more on a running play.

G. Find the probability of losing yardage on a running play.

H. Find and interpret the expected value, or mean of the distribution.

I. Determine the standard deviation of the distribution.

X -4 -2 -1 0 1 2 3 4 6 8 10 15 30 50 99 P(x) .020 .060 .070 .150 .130 .110 .090 .070 .090 .060 .050 .085 .010 .004 .001

Explanation / Answer

f)

P( x . =10) = .050 + .085 + .010 + .004 + .001

= 0.15

g)

P( X< 0 ) = .070 + .060 + .020 = 0.15

h)

E(x) = -4 * .020 + -2 * .060 + -1 * .070 + 0 * .150 + 1 * .130 + 2 * .110 + 3 * .090 + 4 * .070 + 6 * .090 + 8 * .060 + 10 * .050 + 15 * .085 + 30 * .010 + 50 * .004 + 99 * .001

= 4.024

i )

Variance = ( -4 - 4.024)^2 * .020 +  ( -2- 4.024)^2 * .060 +  ( -1 - 4.024)^2 * .070 +  ( 0 - 4.024)^2 * .150 +    ( 1 - 4.024)^2 * .130 +  ( 2 - 4.024)^2 * .110 +  ( 3 - 4.024)^2 * .090 +  ( 4 - 4.024)^2 * .070 + ( 6 - 4.024)^2 * .090 + (8 - 4.024)^2 * .060 + ( 10 - 4.024)^2 * .050 +  ( 15 - 4.024)^2 * .085 +   ( 30 - 4.024)^2 * .010 +( 50 - 4.024)^2 * .004 +  ( 99 - 4.024)^2 * .001

= 46.9434

std.deviation = sqrt ( variance)

= sqrt ( 46.9434)

= 6.852

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