Round all answers to 2 decimals when appropriate A certain tennis player makes a successful first serve 68% of the time. Assume that each serve is independent of the others. She averages 83 1st serves per match. a) Out of 83 first serves, what is the probability that she makes 48 good 1st serves or fewer? b) Find the mean and standard deviation for the number of good 1st serves out of 83 attempts. c) Does the normal approximation apply? Explain. d) Use the normal distribution to find the probability that she gets 48 good 1st serves or fewer out of 83 attempts.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Round all answers to 2 decimals when appropriate
A certain tennis player makes a successful first serve 68% of the time. Assume that each serve is independent of the others. She averages 83 1st serves per match.
a) Out of 83 first serves, what is the probability that she makes 48 good 1st serves or fewer?
b) Find the mean and standard deviation for the number of good 1st serves out of 83 attempts.
c) Does the normal approximation apply? Explain.
d) Use the
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 10 images
