Question

A certain tennis player makes a successful first serve 70% of the time. Assume that each...

A certain tennis player makes a successful first serve 70% of the time. Assume that each

serve is independent of the others. If she serves 7 times, answer the following questions.

a. Verify the distribution of X, the number of first serves in. (Check the binomial conditions.)

b. What is the mean number of first serves in?

c. Find the probability that she gets at least 5 first serves in.

Homework Answers

Answer #1

a) As each serve made is independent of the other serves, and the probability of successful serve made is equal for each of the serve trial. Also there is a fixed number of served made that is 7 here. Therefore the distribution here is a binomial distribution given as:

b) The mean number of first serves is computed here as:

Mean = np = 7*0.7 = 4.9

Therefore, 4.9 is the mean number of first serves in here.

c) The probabiltiy that she gets at least 5 first serves in is computed here as:

= P(X = 5) + P(X = 6) + P(X = 7)

Therefore 0.6471 is the required probability here.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A certain tennis player makes a successful first serve 67% of the time. Assume that each...
A certain tennis player makes a successful first serve 67% of the time. Assume that each serve is independent of the others. If she serves 7 ​times, what's the probability she gets​ a) all 7 serves​ in? b) exactly 4 serves​ in? c) at least 5 serves​ in? d) no more than 4 serves​ in?
A certain tennis player makes a successful first serve 61​% of the time. Assume that each...
A certain tennis player makes a successful first serve 61​% of the time. Assume that each serve is independent of the others. If she serves 5 ​times, what's the probability she gets​ a) all 5 serves​ in? b) exactly 3 serves​ in? c) at least 3 serves​ in? d) no more than 3 serves​ in?
A certain tennis player makes a successful first serve 61​% of the time. Suppose the tennis...
A certain tennis player makes a successful first serve 61​% of the time. Suppose the tennis player serves 70 times in a match.​ What's the probability that she makes at least 56 first​ serves? The probability she makes at least 56 first serves is nothing.
incorrect, Instructor-created question A certain tennis player makes a successful first serve 75​% of the time....
incorrect, Instructor-created question A certain tennis player makes a successful first serve 75​% of the time. Assume that each serve is independent of the others. If she serves 7 ​times, what's the probability she gets​ a) 6 serves​ in? b) at least exactly 5 serves​ in? ​a) The probability she gets exactly 6 serves in is 0.311. ​(Round to three decimal places as​ needed.) ​b) The probability she gets at least 5 serves in is 0.756. ​(Round to three decimal...
A certain tennis player makes a successful first serve 71% of the time. Suppose the tennis...
A certain tennis player makes a successful first serve 71% of the time. Suppose the tennis player serves 110 times in a match. What's the probability that she makes at least 89 first serves? The probability she makes at least 89 first serves is . ? (Use the answers from part a to find this answer. Round to four decimal places as needed.)
A certain volleyball player makes a successful serve 80% of the time. Assume that each serve...
A certain volleyball player makes a successful serve 80% of the time. Assume that each serve is independent of the others. If she serves 7 times, use the information on her serve and the MINTAB results to answer questions 1-3: Cumulative Distribution Function n = 7 and p = 0.8 x P( X <= x ) 0      0.00001 1      0.00037 2      0.00467 3      0.03334 4      0.14803 5      0.42328 6      0.79028 7      1.00000 Describe the random variable, X. Define random Variable...
Everyday Jo practices her tennis serve by continually serving until she has had a total of...
Everyday Jo practices her tennis serve by continually serving until she has had a total of 50 successful serves. If each of her serves is, independently of previous ones, successful with probability 0.4, approximately what's the probability that she will need more than 100 serves to accomplish her goal? Please solve this problem by using normal approximation of binomial distribution only. (Hint: Imagine even if Jo is successful that she continues to serve until she has served exactly 100 times....
A tennis player has two chances to get a serve into play. If the first serve...
A tennis player has two chances to get a serve into play. If the first serve is out, the player serves again. If the second serve is also out, the player loses a point. Here are the probabilities based on four years of Wimbledon Championship: P(1st serve in) = 0.59, P(win a point|1st serve in) = 0.71, P(2nd serve in|1st serve out) = 0.86, P(win a point|1st serve out and 2nd serve in) = 0.59. a. Draw an accurate, properly...
Assume a college basketball player makes 75% of his free throws and that the outcome of...
Assume a college basketball player makes 75% of his free throws and that the outcome of free throw attempts are independent. a) The basketball player is fouled and is awarded two free throws. Develop a probability distribution for number of points (free throws made) for the two attempts. b) The basketball player is fouled and is awarded two free throws. What is the expected number of points for the two attempts? c) The basketball player is fouled and is awarded...
Attempt 2 Stephen is a basketball player who makes 82 % of his free throws over...
Attempt 2 Stephen is a basketball player who makes 82 % of his free throws over the course of a season. Each day, Stephen shoots 70 free throws during practice. Assume that each day constitutes a simple random sample, SRS, of all free throws shot by Stephen, and that each free throw is independent of the rest. Let the random variable X equal the count of free throws that Stephen makes. Compute the probability that Stephen makes at least 56...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT