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Chapter 6: Q 30. (page 373)

Ace! Professional tennis player Novak Djokovic hits the ball extremely hard. His first-

serve speeds follow an approximately Normal distribution with mean 115milesper hour

(mph) and standard deviation 6mph. Choose one of Djokovic鈥檚 first serves at random. Let

Y = its speed, measured in miles per hour.

a. Write the event 鈥渟peed is between 100 and 120 miles per hour鈥� in terms of Y. Then find

this probability.

b. Find the value of c such that P(Y鈮�c)=0.15

Short Answer

Expert verified

a) The probability for the event 鈥渟peed is between 100 and 120 miles per hour鈥� in terms of Y is 79.05%.

b) The units of the data values are miles per hour and thusc=108.76.

Step by step solution

01

Step 1. Given information. 

We have given values of mean渭=115 standard deviation 蟽=6and x=100or120

Let Yrepresents the speed.

02

 a) Step 2. To find the probability. 

The z- score is the value decreased by the mean, divided by the standard deviation .

z=x-渭蟽=100-1156=-2.50z=x-渭蟽=120-1156鈮�0.83

Now,

P(100<Y<120)=P(-2.50<Z<0.83)=P(Z<0.83)-P(Z<-2.50)=0.7967-0.0062=0.7905=79.05%

03

b) Step 3.To find the value of c. 

We have,

P(Y鈮�c)=0.15z=-1.0+.04z=-1.04

Now,

z=x-渭蟽=c-1156c-1156=-1.04c-115=-1.04(6)c=115-1.04(6)c=108.76

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Most popular questions from this chapter

Airlines typically accept more reservations for a flight than the number of seats on the plane. Suppose that for a certain route, an airline accepts 40reservations on a plane that carries 38passengers. Based on experience, the probability distribution of Y=the number of passengers who actually show up for a randomly selected flight is given in the following table. You can check that 渭Y=37.4and蟽Y=1.24.

There is also a crew of two flight attendants and two pilots on each flight. Let X=the total number of people (passengers plus crew) on a randomly selected flight.

a. Make a graph of the probability distribution of X. Describe its shape.

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a. Explain why L can be modeled by a binomial distribution even though the sample was selected without replacement.

b. Use a binomial distribution to estimate the probability that 15 or more students in the sample are left-handed.

Swim team Hanover High School has the best women's swimming team in the region. The 400meter freestyle relay team is undefeated this year. In the 400-meter freestyle relay, each swimmer swims 100meters. The times, in seconds, for the four swimmers this season are approximately Normally distributed with means and standard deviations as shown. Assuming that the swimmer's individual times are independent, find the probability that the total team time in the 400meter freestyle relay is less than 220seconds.follow the four step process.

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Spell-checking Spell-checking software catches 鈥渘onword errors,鈥� which result in a string of letters that is not a word, as when 鈥渢he鈥� is typed as 鈥渢eh.鈥� When undergraduates are asked to write a 250-word essay (without spell-checking), the number Y of nonword errors in a randomly selected essay has the following probability distribution

Part (a). Write the event 鈥渙ne nonword error鈥� in terms of Y. Then find its probability.

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Red light! Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55%chance that the light will be red on a randomly selected work day. Suppose we choose 10 of Pedro's work days at random and let Y=the number of times that the light is red.

a. Explain why Yis a binomial random variable.

b. Find the probability that the light is red on exactly 7 days.
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