Question

Study guide help?

1. The probability that Garrett achieves a field goal on one kick is 0.83
Garrett kicks a football three times in a row.
-Create a probability distribution for X the number of times Garrett kicks a field goal. show how you Obtained each probability. round each probability to three decimal places
-find the probability that at least two of Garretts kicks result in field goals show your work or explain your answer

2. Company A packages roofing nails and boxes that are normally distributed with a mean of 272 nails and a standard deviation of 5.4 nails.
Company B packages roofing nails in boxes that are normally distributed with a mean of 249 nails and a standard deviation of 3.8 nails
Which company is more likely to produce a box of 260 roofing nails explain your answer using Z sources.

Im currently struggling with this and any type of explanation and answer will help!! Thank you!

Answer 1

Explanation:

Garrett achieves a field goal is independent of each kick. Hence X no of kicks is binomial with p = 0.83, and q =0.17

No of trials 3

Hence X can take values as 0 ,1,2,3 and

`P(X=r) = 4Cr(0.83)^r (0.17)^(4-r)`

, r=0,1,2,3

Using the above we obtain prob distribution as

X 0 1 2 3

P(X) 0.0049 0.0720 0.3513 0.5718

P(X>=2) =P(X=2,3,4) =0.9231

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2) Z value for company A =
`(260-272)/(5.4) =-2.22`

Z value for company B =
`(260-249)/3.8 =2.89`

From z value probablility is more for company A as

P(Z>-2.22) >P(Z>2.89)