Applied Math 40S April 10, 2008

We're going to warm up this morning with a wee little quiz ... really, just a little one ... only three questions ... it's not that bad ... honest. ;-)

(1) Find the percent of z-scores in a normal distribution (non-standard) with μ = 75 and σ = 10 that are between:

(c) less than 69

(b) greater than 71

(a) 70 and 80

(2) Find the probability that a randomly selected individual has an IQ between 108 and 130, if the population is distributed normally with a mean of 100 and standard deviation of 16. Write your answer in decimal form rounded to three decimal places. Include a sketch with your answer.

(3) The probability that a student owns a CD player is 3/5. If eight students are selected at random, what is the probability that:

(c) none of them own a CD player?

(b) all of them own a CD player?

(a) exactly four of them own a CD player?

We now want to use the normal approximation of a binomial distribution. The distribution will be approximately normal if:

Once we know that a binomial distribution can be approximated by a normal curve we can calculate the values of μ and σ like this:

np ≥ 5 and nq≥ 5

Normal Approximation to the Binomial Distribution

this is the LINK

between these two

types of distributions

Link by flickr user jontintinjordan

A laboratory supply company breeds rats for lab testing. Assume that male and female rats are equally likely to be born.

(a) What is the probability that of 240 animals born, 110 or more will be female?

Question #4Solve the following binomial problem as normal distribution problem

A laboratory supply company breeds rats for lab testing. Assume that male and female rats are equally likely to be born.

(c) Compare the above answers to #3b and #3c.

(b) What is the probability that of 240 animals born, 120 or more will be female?

Question #4Solve the following binomial problem as normal distribution problem

Solve the following problem using a binomial solutionQuestion #3

(a) What is the probability that of 240 animals born, exactly 110 will be female?

(b) What is the probability that of 240 animals born, 110 or more will be female?

A laboratory supply company breeds rats for lab testing. Assume that male and female rats are equally likely to be born.

The probability that a motorist will use a credit card for gas purchases at a large service station on the Trans Canada Highway is 7/8. If eight cars pull up to the gas pumps, what is the probability that:

(b) four of them will use a credit card?

(a) seven of them will use a credit card?

HOMEWORK

A ferry boat captain knows from past experience that 35% of the passengers will get sick in the rough water ahead. The ferry has 126 passengers. What is the probability that at least 50 passengers will get sick?

(a) Solve this as a binomial distribution problem.

A ferry boat captain knows from past experience that 35% of the passengers will get sick in the rough water ahead. The ferry has 126 passengers. What is the probability that at least 50 passengers will get sick?(b) Solve this as a normal distribution problem. i.e. a normal approximation of the binomial distribution.

(c) Compare your results in (a) and (b). How do they compare?

A handy little applet ...

http://onlinestatbook.com/stat_sim/index.html

Solve a Binomial Problem as an Approximation to a Normal Distribution Problem

According to a group promoting safer driving habits, 63% of all drivers in Manitoba wear seatbelts when driving. During a Safety Week road check, 85 cars were stopped. What is the probability that from 50 to 60 (inclusive) drivers were wearing seatbelts.

HOMEWORK

A toy manufacturer produces balloons that have a 3 percent defective rate. In a shipment of 4000 balloons, what is the probability that:

(b) between 100 and 130 balloons inclusive will be defective?

(a) fewer than 100 balloons will be defective?

Use a normal approximation to solve this problem.HOMEWORK

The manager of the Jean Shop knows that 3 percent of all jeans sold will be defective, and the money paid for these pairs of jeans will be refunded. The manager went on holidays for a period of time, and an employee sold 247 pairs of jeans. The employee reported that refunds were given for 14 pairs of jeans.

(c) Does the employer have proof that the employee did something wrong?

(b) Does the employer have reason to be suspicious of the employee?

(a) What is the probability that 14 pairs of jeans were defective?

HOMEWORK

A producer of hatching eggs acknowledges that 4 percent of all the eggs produced will not hatch. In a shipment of 600 eggs, what is the probability that:

(c) between 20 and 24 inclusive will not hatch?

(b) fewer than 20 will not hatch?

(a) at least 25 will not hatch?

HOMEWORK