Statistics and Probability Answers

1. A high school counselor wants to examine whether the teenage pregnancy rate at her school is different from the rate nationwide. She knows that the rate nationwide is 15 %. She randomly selects 80 female students from her high school. She finds that 9 out of 80 students are either pregnant now or have been pregnant previously.

a. What statistical test should be used to analyze the data?

b. Identify H0 and Ha for this study


c. Conduct the appropriate analysis
d. Should H0 be rejected? What should the researcher conclude?

Ten cards numbered 1 to 10 are mixed in a hat.Two cards numbered p and q are drawn from the hat.What is the probability that p+q=10?
a) 2/5
b) 4/9
c) 7/45
d) 4/45

A committee of four is to be formed from among 5 economists, 6 engineers, 3 statisticians and 1 doctor . Find the probabilities that,
(i) Each profession is represented in the committee
(ii) It has a doctor and at least one economist
(iii) It has a doctor and at least one economist and others from remaining members

The probbability of having a head cold is 5% and 1000 people are checked at random what is the probability that at least 60 people have head colds?

A student has the opportunity to take a test at most thrice.the student knows that each time he takes the test,his score is an independent random draw from the uniform distribution on the interval [0,100].
After learning his score on a test,the student can either stop and accept it as his official score,or he can discard the result and retake the test.If the student rejects his score twice and takes the test a third time,that score will be his official score.
If his objective is to maximise his expected official score,the student will decide to be retested after the very first test if and only if his score is less than....
a. 50
b. 62.5
c. 75
d. 87.5

explain

suppose X and Y are independent random variables that follow the uniform distribution on the interval [0,1]. Let Z=min{X,Y}. P(Z<0.5)=?

A test has mean of 90, standard deviation of 8 and administered to 240 students. The scores are normally distributed. How many students fell between a z score of 0 and 1.0?

3. The mean time taken by all participants to run a road race was found to be 220 minutes with a standard deviation
of 20 minutes. Using the 68 – 95 – 99.7 Rule, find the percentage of runners who ran this race:

a. In less than 180 minutes
b. In more than 220 minutes
c. In between 160 and 280 minutes
d. In at least 240 minutes
e. In no more than 200 minutes

A personnel manager has found that historically the scores on aptitude tests given to applicants for entry- level positions follow a normal distribution with a standard deviation of 32.4 points. A random sample of nine test scores from the current group of applicants had a mean score of 187.9 points.
a. Find an 80% confidence interval for the population mean score of the current group of applicants.
b. Based on these sample results, a statistician found for the population mean a confidence interval extending from 165.8 to 210.0 points. Find the confidence level of this interval.

Explain the rolling of a fair die and then flipping of a fair coin with the help of tree diagram.