Statistics and Probability Answers

The probability that kodjo and adogba pass an examination are 3/4 and 3/5 respectively. Find the probability of both boys failing the examination.
a)1/3
b) 3/10
c) 9/20
d) 1/3

A sample of 64 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population.

The average monthly electric bill of a random sample of 100 residents of a city is $90 with a standard deviation of $24. Construct a 95% confidence interval for the mean monthly electric bills of all residents.

The average monthly electric bill of a random sample of 100 residents of a city is $90 with a standard deviation of $24. Construct a 90% confidence interval for the mean monthly electric bills of all residents.

A researcher studies the number of steps college students take per day. She finds that the number of steps college students take per day has a Normal distribution with a mean of 5500 and standard deviation 1600. She believes students who do not live on campus take more steps than those who do live on campus. Write both the null hypothesis and the alternative hypothesis she would use to verify her suspicion

The density function of a continuous random variable X is given by

Ae^(-x) , 0≤x≤1
f(x)= 0 , otherwise


Evaluate the following:
a) Mean
b) Variance
c) E [(2+3x)^2]

If a random variable X has a cumulative distribution function F(x) given by

0 , x≤0
F(x) = c (x-e^(-x)) , 0<x<1
5 , x≥1


then find its corresponding probability distribution function and hence calculate
P(0<x<1)

A researcher is interested in determining if the method of execution (lethal injection vs. electrocution) affects whether a criminal is sentenced to life or death.

The Null Hypothesis is [x].

Police estimate that 80% of drivers wear their seatbelts. They set up a safety road block stopping, cars to check for seatbelt use. If they stop 9 cars, what is the probability that:
1.1) Exactly three drivers are not wearing their seatbelts?
1.2) At least 3 drivers are not wearing their seatbelt?
1.3) At least 2 drivers but no more than 4 drivers are not wearing their seatbelt?

scores made by employees on a manual dexterity test are normally distributed with a mean of 600 and a variance of 10 000.
a) What proportion of employees taking the test score below 300
b) An employee is about to take a test. What is the probability that the employee's score will be 850 or more.
c) What proportion of employees score between 450 and 700?
d) Suppose that management decides to consider for promotion only those employees who make a score of 800 or more. If the company has 800 employees how many will be eligible to be considered for promotion?