Explain and show work for each part. 3. Mike and Ike decide to have a basketball

Question

Explain and show work for each part.

3. Mike and Ike decide to have a basketball shooting contest, and they decide shoot three pointers. Ike truly makes 40% of his three point shots, while Mike truly makes 30% of his three point shots. It is safe to assume each shot is independent from the next. a. What is the probability the Mike makes at least one of his first 5 three pointers? b. They decide to shoot 50 three pointers apiece. What are the mean and standard deviation for the number of three pointers that Mike will make in 50 three point shots? c. What is the approximate probability that Kevin will make at least 20 of his 50 three point shots?

Explanation / Answer

a) probability that mike makes at least one of first 3 pointers =1-P(he makes none from his first 5)

=1-(1-0.3)5 =0.8319

b)for mean =np =50*0.3 =15

and std deviation =(np(1-p))1/2 =(50*0.3*(1-0.3))1/2 =(10.5)1/2 =3.2404

c)we will apply normal approximation for calculating above probability

for normal distribution z =(X-mean)/std deviation

hence probability that Kevin will make at least 20 out of his 50 three point shots

=P(X>=20) =1-P(X<=19.5) =1-P(Z<(19.5-15)/3.2404)=1-P(Z<1.3887)=1-0.9175 =0.0825

please revert for any clarification required.

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