Statistics and Probability Answers

The probability of x,y and z becoming managers are 4/9 ,2/9 and 1/3 respectively.The probabilities that the bonus scheme will be introduced if x,y and z becomes managers are 3/10 ,1/2 ,and 4/5 respectively

(a)what is the probability that the bonus scheme will be introduced?

(b)if the bonus scheme has been introduced,what is the probability that the manager appointed was x

The weights of students in a certain school are normally distributed with a mean weight of 66 kg. 10% have a weight greater than 70kg. What percentage of students weighs between 52kg and 66kg?  

How did we get our answer for this problem above? 

A population consists of the values {1, 2, 3, 4, 5). Consider samples of size 3 that can be drawn

from this population.

a. List down all the possible samples and corresponding sample mean

Sample

Sample Means

5

b. Construct the sampling distribution of the sample means.

Sample Means Frequency

Probability P(x)

c. Draw a histogram of the sampling distribution of the sample mean.

A course in mathematics is taught to 15 students by explicit method. Another group of 17 students was given the same course by means of another method. At the end of the semester, the same test was administered to each group. The 15 students under method A made an average of 85 with a standard deviation of 4, while the 17 students under method B made an average of 81 with a standard deviation of 5. Test

the null hypothesis of no significant difference in the performance of the two groups of

students at 5% level of significance.

Solution:

1. H0:

H1:

2. Level of Significance:

3.Test:

4. Critical Region:

5. Solution:

Make a decision and draw a

conclusion based from the results.

1. Decision:

2. Conclusion:

A manufacturer of a brand of designer jeans has pitched her advertising to develop an

expensive and classy image, the suggested retail price is Rs 750. However, she is concerned

that retailers are undermining her image by offering jeans at discount prices. To better

understand what is happening, she randomly sampled 15 retailers who sell her product and

determines the price. The data collected is as follows:

670 720 700 570 780 770 670 720 730 770 720 810 730 790 750

Find the 95% confidence interval estimate for the prices.

A sample of students from an introductory psychology class were polled regarding the

number of hours they spent studying for the last exam. The data was used to make

inferences regarding the other students taking the course. There data are below:

8, 22.7, 14.5, 9, 9, 3.5, 8, 11, 7.5, 18,

20, 7.5, 9, 10.5,15, 19, 9, 8.5, 14,20

Compute a 99% confidence interval.

a farmer produces seeds in pckets for sale. the provbility that seed selected at random will grow is 4/5. if 20 seeds are sown what is the probability that

(A) less than 2 will grow

(B) Less than 2 will not grow

(C) Exactly half the seed will grow

(d) exactly 2 will grow

> Find the mean of the population

> Find the mean of the sampling distribution of the

sample means

> find the Variance of the population

> find the Variance of the sampling distribution of the

sample mean

> find the Standard deviation of the population

> find the Standard deviation of the sampling

distribution of the sample mean

STUDENT

A

B

C

D

E

HEIGHT (IN CM)

120

130

110

125

159

> Find the mean of the population

> Find the mean of the sampling distribution of the

sample means

> find the Variance of the population

> find the Variance of the sampling distribution of the

sample mean

> find the Standard deviation of the population

> find the Standard deviation of the sampling

distribution of the sample mean

STUDENT HEIGHT (IN CM)

A 120

B 130

C 110

D 125

E 159

If we toss two balanced dice, and let A be the event that the sum of the face values

of two dice is 8, and B be the event that the face value of the first one is 3. Calculate

P(A/B).