Statistics and Probability Answers

Q3. a. If a random variable X has mean 3 and standard deviation 5, then find out the variance of a variable

Y=2X-5.

b. If each observation in the set of values (X, Y) is divided by 100, then find the correlation coefficient of

new data set?

Q2.a. Suppose a large number of people take a test, and every single student gets exactly half of the answers

right. In this case, find out the standard deviation?

b. Image that 11 people take a 10 question test. Suppose one student gets 10 correct answers, one gets 9

correct, one gets 8 correct, and so on, all the way down to one student getting none correct. What is

the median score, accurate to three decimal places?

c. Draw an appropriate graphs for the given data set, grouped as: even and odd.

-5, 4, 1, -4, 0, 3, 2, -2, 5, -3,-1,-2.

d. Find out the appropriate measures of location for the given data set:

Classes 7.5- 12.5 12.5-17.5 17.5-22.5 22.5-27.5 27.5-

Frequency 3 15 19 3 15

e. The coefficient of skewness of a series A is 0.15 and that of series B is 0.062. Which of the two series

is less skewed?

Dog 1 2 3 4 5 6 7 8 9

Weight 0.41 1.48 0.79 0.41 0.85 1.11 0.37 1.11 0.41

Consumption in cups 3 8 5 4 5 6 3 6 3

Dog 10 11 12 13 14 15 16 17 18

Weight 0.91 1.09 2.07 0.49 1.13 0.84 0.95 0.57 1.68

Consumption in cups 5 6 10 3 6 5 5 4 9

a. Calculate that, is there any linear relationship between dog weight and consumption of food?

b. How much does ten pounds of weight change the estimated number of cups of dog food consumed?

c. What would be the weighted mean of n natural numbers if weights are the corresponding numbers?

d. Which type of relationship between age and church attendance exist, if older people are less likely to

attend church than younger people?

Imagine that 11 people take a 10 question test. Suppose one student gets 10 correct answers, one gets 9  correct, one gets 8 correct, and so on, all the way down to the student getting none correct. What is the mean score, accurate to three decimal places?

The standard deviation of marks of 100 students is 13. Every student is awarded later 5 or more marks.        

 Find out the standard deviation of the new set of marks?

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. What is the probability that the height of a child, picked at random, has a between 110 cm and 122 cm?

A study discussed that the percent purity of oxygen from a certain supplier yields a mean of 99.61% and a standard deviation of 0.08%. If the distribution of percent purity is said to be in normal distribution, what purity value exceed exactly 5% of the population?

n= 1000, n= 60, mean = 75, standard deviation= 6, probability= p(x<76.5)

Find each of the following percentile points under the normal curve.

1. P₉₉

2. P₉₀

3. P₆₈

4. P₄₀

5. P₃₂

The Coronavirus Disease (COVID-19) is an infectious disease caused by a new strain of

coronavirus. The World Health Organization (WHO) claims that the incubation period of the virus

in the infected person has a mean of 5.1 days. The doctors in the Philippines conducted a

research and they found out that incubation period of the virus in human body is 6.03 days with a

standard deviation of 3.32. The samples were 46 COVID patients. Is there enough evidence to

conclude that the incubation period of the virus is 5.1 days as stated, at α = 0. 01?

Prove the claim using this graphic organizer.

Given:

State the null  and alternative  hypothesis

Determine the  test statistics,  compute its  

value

Find the critical  value and draw  the critical  

region. 

(Draw the  

figure)

Draw  

conclusion