Statistics and Probability Answers

Find the corresponding area between 𝑧 = 0 and each of the following.

1. z = 0.85

2. z = 1.27

3. z = 2.86

4. z = −1.05

5. z = −2.96

In a time and motion study, it was found that a certain manual work can be finished at an average time of 40 minutes with a standard deviation of 8 minutes. A group of 16 students is given a special training and then found to average only 35 minutes. Can we conclude that the special training can speed up the work using 0.01 significance level?

A worn machine is known to produce 10% defective components. If the random

variable X is the number of defective components produced in a run of 4 components, find the probabilities that X takes the values 0 to 4.

An elevator in the hospital has a weight limit of 1650 pounds. Suppose an average weight of

the people who use this elevator is 140 pounds with a standard deviation of 25 pounds.

Assuming that the distribution of weights is approximately normal and a random sample of

11 people are selected, what is the probability that the random sample will exceed the weight

limit?

1.In a group of 40 subjects screened for non- communicable diseases, 10 are healthy and every person of the remaining 30 has either high blood pressure, a high level of cholesterol or both. You were further informed that 27 have high blood pressure and 25 have a high level of cholesterol.

ii. If a person is selected randomly from this group of subjects, what is the probability that he or she has either high blood pressure or high level of cholesterol?

2. In a group of 60 subjects screened for non- communicable diseases, 20 are healthy and every person of the remaining 40 has either high blood pressure, a high level of cholesterol or both. You were further informed that 15 have high blood pressure and 25 have a high level of cholesterol. If a person is selected randomly from this group of subjects, what is the probability that he or she has either high blood pressure or high level of cholesterol or both using the additive rule of probability.

3. a) Three messages A, B, C have probabilities 0.4, 0.3 and 0.3 respectively, of their

occurrences. If total 100 massages are sent out, calculate the total information (Itotal)

carried by them. Also calculate the entropy of the signal.

10. Which of the following statements are true? Give reasons for your answer. (10)

(i) F-distribution is always used in goodness of fit.

(ii) Measure of central tendency in a data set refers to the extent to which the

observations are scattered.

(iii) A process is said to be under assignable cause when the points are above the VCL

link of ( chart. X,R)

(iv) Simple random sampling is done by using random number tables where the

probability of drawing a digit is .1 0⋅

(v) All time series have a trend.

9c) A researcher measures the temperature of a solution 5 times. The observations are

25, 32, 27, 29, 30 o

C. Determine an unbiased estimate of the temperature.

9b) A box contains 10 screws, 3 of which are defective. Two screws are drawn at

random. Find the probability that none of them is defective, if the sample is drawn

(i) with replacement,

(ii) without replacement.

9. a) A manufacture of rayon wants to compare that the yield strength of 5 11⋅ kg/ 2 mm is

met or not at 5% level of significance. The manufacturer draws a sample and

calculates the mean to be 8 12⋅ kg/ 2 mm and the standard derivation is known to be

2⋅0kg/ mm .

2

Carry out the statistical test appropriate for this.