Statistics and Probability Answers

1.     Samuel woke up late in the morning on the day that he has to go to school to take an important test. He can either take the shuttle bus which is usually running late 15% of the time or ride his unreliable motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice.

a.      If Samuel, in fact, gets to the test on time, what is the probability that he took the bus? (2)

(b)If Samuel is late to the test, what is the probability that he took the bus?

The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls.

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x P(x)

0 0.005

1 0.018

2 0.044

3 0.117

4 0.198

5 0.245

6 0.206

7 0.114

8 0.037

9 0.015

10 0.001

A statistics teacher knows from past experience that a student who does homework consistently has a probability of 0.95 of passing the examination , whereas a student who does not do homework has a probability of 0.30 of passing.

i) If 25% students in a large group of students do their homework consistently, what percentage can expect to pass?

ii) If a student chosen at random from the group gets a pass, what is the probability that the student has done the homework consistently?

A speaks the truth in 80% of the cases and B in 70% of the cases. In what percentage of cases are they likely to contradict and do not contradict each other in stating the same fact?

The odds against student A solving a business statistics problems are 4:3 and odds in favor of student B solving the same problem are 7:8.

i) what is the chance that the problem will be solved if they both try?

ii) What is the probability that neither solves the problem?

a certain type of battery has a mean shelf life of 600 days with a standard deviation of 28 days

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the time for a major exam to be completed is normally distributed with an average of 55 minutes and a standard deviation of 9 minutes. If 92% of the student completed the exam, when should the test be terminated?

Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Find the values of the random variable Z.

the time for a major exam to be completed is normally distributed with an average of 55 minutes and a standard deviation of 9 minutes. If 92% of the student completed the exam, when should the test be terminated?