Statistics and Probability Answers

The height of grade 1 pupils are approximately normally distributed with µ = 45 inches and s = 2.

1. If an individual pupil is selected at random, what is the probability that he or she has a height of 42 and 47?
2. A class of 30 of these pupils is used as a sample. What is the probability that the class mean is between 42 and 47?
3. If a pupil is selected at random, what is the probability that is taller than 46 inches?
4. A class of 30 of these pupils is used as sample. What is the probability that the class mean is greater than 46 inches?

State whether the following statements are true or false and reason for support it

(1) If the level of significance is the same, the area of the rejection region in a two tailed test is less than that in a one tailed test.

(2)Non parametric tests are more powerful than the parametric tests

(3)If T1 and T2 are two estimators of the parameter theta such that varience of T2 =1/n and varience of T2=n then T1 is more efficient than T2

A 95% confidence interval is smaller than 99% confidence interval. State whether the given statement is true or false give reason in support of answer

A petrol station has two pumps. The service time follows the exponential distribution with mean 4 minutes and cars arrive for service in a Poisson process at the rate of 10 cars per hour. Find the probability that a customer has to wait for service. What proportion of time the pump remains idle?  

a)     A supermarket has two girls ringing up sales at the counters. If the service time for each customer is exponential with mean 4 minutes and if the people arrive in Poisson fashion at the rate of 10 per hour

a)        What is the probability of having to wait for service?                       

 b)       What is the expected percentage of idle time for each girl?              

 c) If a customer has to wait, what is the expected length of his waiting time?

if two coins and a dice are thrown at once, what is the probability of getting two heads and six or one tail, one head and a three?

1.determine the area and show this graphically

A. To the right of z=1.3

B. Between z=-1 and z=-2.3

2.find each of the following percentile points under the normal curve complete your procedure

A. P79

B. P90

A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. What is the probability that the individual waits more than 7 minutes?

7. In 1900, W. Y. Kevin published the article “The anticipated Error of a Mean”. In this pioneering paper, written under the pseudonym “Student,” Kevin introduced what later became known as Student’s t-distribution. Kevin used the following data set, which gives the additional sleep in hours obtained by a sample of 10 patients using laevohysocyamine hydrobromide.

1.9 0.8 1.1 0.1 −0.1

4.4 5.5 1.6 4.6 3.4

a. Obtain and interpret a 95% confidence interval for the additional sleep that would be obtained on average for all people using laevohysocyamine hydrobromide.

b. Was the drug effective in increasing sleep? Explain your answer.

A certain group of welfare recipients receives relief goods with a mean amount of Php 500.00 per week. A random sample of 75 recipients is survived and found that the mean amount of relief goods they received in a week is Php 600 and a standard decision of Php. 50.00. Test the claim at 1% level of significance is not Php 500.00 per week and assume that the population is approximately normally distributed.

Determine the following

Null and alternative hypothesis:

Critical value and rejection region:

Computed test statistic:

Conclusion: