Statistics and Probability Answers

A traffic study of 1,600 vehicles that passed by a checkpoint showed that their speeds were normally distributed with a mean of 97.6 kph and a standard deviation of 10.4 kph. How many vehicles had a speed of more than 100 kph?

Several intelligence tests follow a normal distribution with a mean of 100 and a standard deviation of 15.

a) Determine the percentage of the population that would obtain a score between 95 and 110.

b) What interval centered at a score of 100 contains 50% of the population?

c) For a population of 2,500, how many are expected to have a score above 125?

Find the mean and the standard deviation of the heights of male engineering students in which the heights 66 inches and 75 inches correspond to standard score of -0.6 and 1.1, respectively.

A research firm conducted a survey to determine the mean amount of money smokers spend on cigarettes during a day. A sample of 100 smokers revealed that the sample mean is N$ 5.24 and sample standard deviation is N$ 2.18 Assume that the sample was drawn from a normal population.

2.1) Find the point estimate of the population mean (2)

2.2) Determine the lower limit of the 95% confidence interval for estimating the unknown population mean. (5)

2.3) Determine the upper limit of the 95% confidence interval for estimating the unknown population mean. (3)

2.4) Find the width of the 95% confidence interval for estimating the unknown population mean (2)

2.5) Use the data provided above to test a claim at a 1 % Level of Significance that the unknown population mean of spending amount on cigarettes is N$ 5.00 (8)

Molecules of a rare gas occur at an average rate of 3 per cubic metre of air and follow a poisson distribution.
i) Find the probability that 3 cubic metre of air contain exactly 4 of the molecules
ii) The probability that at least one molecule is found is 0.99. Find how much air is taken as a sample.

How many sample of size 3 are possible out of population size of 8?

A soldier who hits a target with probability 2/3 fires shots until he hits the target or 5 shots have been fired. Let X denote the number of shots fired. Find the
i) probability distribution of X
ii) mean of X

A rectangle with height and width equal to 4 and 25 respectively, is drawn on a checkered
paper. Bazil paints a random horizontal 1 x 3 rectangle, and Peter paints a random vertical 3 x 1
rectangle (each rectangle consists of 3 sells). Find the probability that at least one of the cells is
painted twice. Express the answer in percent, and round to the nearest integer.

A student knows 20 answers from the 25 given questions of the chemistry exam.
What is probability that student will answer not less than 2 questions from 3 ones
taken at random?

A student prepared for the exam only one ticket №10 from 25 given ones. In what
turn it will be better for him to answer: the first, the second or the third?