Statistics and Probability Answers

The owner of a factory that sells a particular bottled fruit juice claims the the average capacity of their product is 250 ml to the test claim a consumer group gets a sample of 100 such bottles calculates the capacity of each bottle and then finds the mean capacity to the be 248ml.The standard deviation is 5ml . Test the hypothesis that the population mean is less that 250 ml. Assumed that the population is normally distributed. Use level of significance level is 0.5 and the z value is 1.645

D. Not to

lat the

e is

nsare.

when, in fact, it is

6. A statistics senior high teacher believes that fewer than 20% of QNHS students answered the

online examination through google forms. He surveys 84 of his students and finds that 11 answered

the online exam. An appropriate alternative hypothesis is:

A. p = 0.20

B. p > 0.20

C. p<0.20

D. p < 0.20

When do we add the two corresponding areas of the z-score?

In an experiment of tossing a fair coin three times, find the P(X=2), P(X > 1) and P(1 ≤ X < 2). Let X be the random variable giving the number of tails.

The number of customers arriving per day at a certain automobile service facility is assumed to follow a Poisson Distribution with mean λ=20. Use normal approximation to find the probability that in a given day.

a) less than 25 customers will arrive;

b) at least 10 customers will arrive;

c) between 15 and 19 inclusive will arrive;

Suppose that X is a binomial random variable with n = 100 and p = 0.1

a) compute the exact probability that X is less than 4.

b) approximate the probability that X is less than 4 and compare to the result in part (a).

c) approximate the probability that 8 < X < 12

A process yields 10% defective items. If 100 items are randomly selected the process, use normal approximation to find the probability that the number of defectives.

a) exceeds 13 and

b) less than 8.

The heights of 1000 students are normally distributed with a mean of 174.5 centimeters and a standard deviation is 6.9 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would you expect to have heights.

a) less than 160.0 centimeters?

b) between 171.5 and 182.0 centimeters inclusive?

c) equal to 175.0 centimeters?

d) greater than or equal to 188.0 centimeters?

A company pay its employees an average wage of $15.90 an hour with a standard deviation of $1.50 , if the wages are approximately normally distributed and paid to the nearest cent,

a) what percentage of the workers receive wages between $13.75 and $16.22 an hour inclusive.

b) The highest 5% of the employee hourly wages is greater than what amount?

What level of measurement is required for this qualitative variables?