A report from the secretary of Health and Human Services sta

A report from the secretary of Health and Human Services stated that 70% of single-vehicle traffic accidents that occur at night on weekends involve an intoxicated driver. If a sample of 15 single-vehicle traffic fatalities that occur at night on a weekend is selected, find the probability that exactly 12 involve a driver who is intoxicated.

Use both Table C and the Binomial Probability formula on page 338

A survey from Teenage Research Unlimited found that 30% of teenage consumers receive their spending money from part –time jobs. If 5 teenagers are selected at random, find the probability that at most 2 of them will have part –time jobs. Use Table C (handout)

A national poll conducted by The New York Times revealed that 80% of Americans believe that after you die, some part of you lives on, either in a next life on earth or in heaven. Consider a random sample of 10 Americans and count x, the number who believe in life after death.

Find P(x = 3)

Find P(x < 7)

Find P(x > 4)

Use CrunchIt; include your printout .

The American College of Obstetricians and Gynecologists report that 22% of all births in the U.S. take place by Caesarian section each year.

In a random sample of 1000 births, how many, on average will take place by Caesarian section?

What is the standard deviation of the number of Caesarian section births in a sample of 1000 births?

R.H. Bruskin Associated Market Research found that 30% of Americans do not think that having a college education is important to succeed in the business world. If a random sample of five Americans is selected, find these probabilities. Use any of the three methods discussed in class. Indicate which one you used.

Exactly two people will agree with that statement.

At most three people will agree with that statement

At least two people will that statement

Fewer than three people will agree with that statement

Which of the following are binomial experiments or can be reduced to binomial experiments? Justify your answer.

Surveying 100 people to determine if they like Sudsy Soap

Tossing a coin 100 times to see how many head occur

Testing four different brands of aspirin to see which brands are effective

Checking 1000 applicants to see whether they were admitted to White Oak College

A magazine reported that 6% of American drivers read the newspaper while driving. If 300 drivers are selected at random,

Find the probability that no more than 15 say they read the newspaper while driving. Use CrunchIt and include your printout

Determine if a normal approximation to the binomial can be used. If so determine the probability and compare it to part a)

Solution

1)  n=15 and p = 0.7.....
probability that exactly 12 involve a driver who is intoxicated = (15 C 12 )* ( 0.7)^12 * ( 0.3)^3 = 0.170040213...

2) n = 5 , p = 0.3...
probability that at most 2 of them will have part –time jobs = prob. [ none of them will have part time jobs ] + p [ 1 of them will have part time job ] + p [ 2 of them have part time jobs ]

= (5 C 0) (0.3)^0 (0.7)^5 + (5 C 1 ) ( 0.3) ^1 *(0.7)^4 + ( 5 C 2)*(0.3)^2*(0.7)^3

= 0.83692.......

3) n=10, X= COUNT AND p = 0.8.....

P(x = 3) = ( 10 C 3) (0.8)^3*(0.2)^7 = 0.000786432.......

Find P(x < 7) = 1 - P( x >=7) = 1 - p( x=7) - p(x=8) - p(x =9) - p(x =10) = 0.1208739.....

P(x > 4) = 1 - P( x<=4) = 0.993631......

4) n=1000 and p = .22....

s.d = sqrt( 0.22*(0.78) / 1000 ) = 0.01309962.....

and average= np = 220..

5) n=5....p = 0.3...

p[ Exactly two people will agree with that statement ] = (5 C 2) (0.3)^2 * ( 0.7)^3 = 0.3087...

P [ At most three people will agree with that statement ] = 1 - P [ 4 people will agree ] - p [ 5 will agree]

= 0.96922

p [ At least two people will that statement ] = 1 - P [ atmost 1 people will inderstand ] = 1 - p [ 1 people will understand ] - p [ 0 people will understand ] = 0.30371.....

p [Fewer than three people will agree with that statement] = p [ 2 people will understand ] + p [ 1 people will ] + p [ 0 people will ] = 0.83692...

6)

Surveying 100 people to determine if they like Sudsy Soap

Tossing a coin 100 times to see how many head occur

Checking 1000 applicants to see whether they were admitted to White Oak College

7) n = 300 and p = 0.06.......

prob [ no more than 15 say they read the newspaper while driving ] = 0.233....

\\

yes..np = 18 whcih is >15 and nq = 282 >15..
so, a normal dist. can be assumed here..

s.d= sqrt( 300*0.06*.94) = 4.11339276

So, P [ X <=15 ] = P [ z < = ( 15-18) / 4.11339276 = P [ z <= - 0.729927 ] = 0.2329015...
so, the prob.s obtained are almost same....