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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!

Respuesta :

Answer:

Step-by-step 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

[tex]P(X=r) = 4Cr(0.83)^r (0.17)^{4-r}[/tex]

, 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 =[tex]\frac{260-272}{5.4} =-2.22[/tex]

Z value for company B = [tex](260-249)/3.8 =2.89[/tex]

From z value probablility is more for company A as

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

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