Statistics and Probability Answers

The distance (in miles) for which a certain type of the tyre is to last is a
random variable with the following pdf

The life time of a certain kind of battery is a random variable which has exponential distribution will mean of 200 hours. Find the probability that such a battery will i) last at most 100 hours i)last any where from 400 to 800 hours.

The life time of a certain kind of battery is a random variable which has exponential distribution will mean of 200 hours. Find the probability that such a battery will i) last at most 100 hours i)last any where from 400 to 800 hours.

A fair spinner has 9 equal sections: 3 red, 2 blue and 4 green.
It is spun twice.
What is the probability of getting red both times?

An agriculturists is trying out a planting technique that he hopes will increase the yield on his orange plants. The average number of pods on one of his orange plants is 118 pods with a standard deviation of 80 pods. This year, after trying his new planting technique, he takes random sample of his plants and fins the average number of pods to be 125. He wonders whether or not this is a statistically significant increase. What are his hypotheses and the test statistic? Use a 0.05 significance level.

The university atheletic director is asked if soccer players are doing as well academically as other students atheletes. We know from a previous study that the average GPA for the student athletes is 3.05. After an initiative to help improve the GPA of student athletes, the athletes director randomly sample 25 soccer players and finds that the average GPA of the sample is 3.10 with a sample standard deviation of 0.34. is there a significant improvement? Use a 0.05 significance level.

2. Of the 38 plays attributed to Shakespeare, 18 are comedies, 10 are tragedies, and 10 are histories. One play is randomly selected from Shapespeare’s 38 plays. Find the odds.

a. In favor of selecting a comedy.


b. In favor of a selecting a tragedy.


c. Against selecting a history.


d. Against selecting a comedy.


e. In favor of selecting a comedy or a tragedy.



f. In favor of selecting a tragedy or a history.



g. Against selecting a tragedy or a history.



h. Against selecting a comedy or a history.

1.One card is randomly selected from a deck of cards. Find the odds.

Against drawing a black king.

2. You are interested in heights of trees on either side of a mountain. You choose a random
sample of ten trees on each side of the mountain and measure their heights in each
sample (Table 1).
Table 1. Heights of trees (m) on the north and south of a mountain
North. South
5.5 3.5
7.0. 3.8
5.0. 4.0
4.0 6.8
6.5 3.3
7.5 6.3
5.8. 6.5
8.0. 7.0
4.0. 6.6
5.4 2.0
Test the data to show whether trees are significantly larger on the northern side of the
mountain at the 5 % significance level. Check that the assumptions are met before choosing
the appropriate test, and give reasons for your choice of test.

1. We are interested to know whether test animals respond to temperature by moving
toward a favoured temperature. Animals were placed in a temperature gradient marked
in units from zero (the starting point) in the middle of the gradient to positive at the
warm end and negative at the cold end. The mean position along the gradient was found
to be -1.352 units, the standard deviation was 12.267 units and n=500 individuals. Is
there a significant tendency to aggregate at either the cold or warm end of the gradient?
Start by setting up a null hypothesis in terms of the mean position along the gradient =
0.