Statistics and Probability Answers

QUESTIONS 20, 21 AND 22 ARE BASED ON THE FOLLOWING INFORMATION.

Suppose A Check conducted further research using a sample size of 100. The number of
times the AI algorithm is successful at detecting fake news is normally distributed with a different
mean of 900 and the same standard deviation of 100. Let X be the number of times the algorithm is successful at detecting fake news.

Question 20

What is the standard error of the mean?

(1) 900
(2) 100
(3) 10
(4) 1
(5) 0

Question 21

What is the mean of the sampling distribution of the mean?

(1) 900
(2) 100
(3) 10
(4) 1
(5) 0

Question 22

P(X ≤ 920) =?

(1) 2.0000
(2) 0.9772
(3) 0.5793
(4) 0.2000
(5) 0.0228

QUESTIONS 16 TO 19 ARE BASED ON THE FOLLOWING INFORMATION.

A Check uses AI algorithm to detect FN. The number of times the algorithm is successful at detecting FN is normally distributed with the mean of 1000 and the standard deviation of 100. Let X be the number of times the algorithm is successful at detecting FN.

Question 16

Choose the incorrect

The probability that X is at most
(1) 800 is 0.0228
(2) 900 is 0.1587
(3) 1000 is 0.0000
(4) 1100 is 0.8413
(5) 1200 is 0.9772

Question 17

What is the probability that X is at least 950?

(1) 0.6915
(2) 0.5000
(3) 0.3085
(4) 0.0000
(5) None of the above

Question 18

What is the probability that X is between 1000 and 1300?

(1) 0.9990
(2) 0.9987
(3) 0.5000
(4) 0.4987
(5) 0.0000

Question 19

A Check knows that the probability that X is at most x is 0.8997 i.e. P(X ≤ x) = 0.8997. What is the value of x?

(1) 1.2
(2) 1.28
(3) 1120
(4) 1128
(5) None of the above

Question 15

Given that P(-2 ≤ Z ≤ z) = 0.4019, what is the value of z?

(1) 0.19
(2) 0.19
(3) 0.4247
(4) 0.5753
(5) None of the above

Question 11

The value of the mean of a normal distribution corresponds to which values on the standard normal curve?

(1) 0
(2) 1
(3) 100
(4) 1000
(5) None of the above.

Question 12

For any normal distribution (according to the empirical rule), approximately what percentage of
values lies within three standard deviations of the mean?

(1) 2%
(2) 68.3%
(3) 95.4%
(4) 99.7%
(5) 100%

Consider the standard normal distribution and answer questions 13 and 14.

Question 13

Which one of the following statements is incorrect?

(1) P(Z = 0) = 0
(2) P(Z ≥ 0) = 0.5
(3) P(Z ≤ 0) = 0.5
(4) P(Z ≤ -1) = 0.1587
(5) P(Z ≥ 1) = 1 - P(Z ≤ -1)

Question 14

P(-1 ≤ Z ≤ 2) =?

(1) 0.1359
(2) 0.4772
(3) 0.8185
(4) 0.8415
(5) None of the above

Suppose that the number of daily FKP is Poisson distributed with the mean of
0.2 posts per day. Use this information to answer questions 8, 9 and 10.

Question 8

What is the probability that on any given day there will be no FKP?
(1) 0.7408
(2) 0.2000
(3) 0.0000
(4) e^0.2
(5) None of the above

Question 9

Which one of the following statements is incorrect?
(1) The probability that there will be one FKP on any given day is 0.1637
(2) The probability that there will be two FKP on any given day is 0.0164
(3) The probability that there will be at least three FKP on any given day is 0.0012
(4) The probability that there will be at least five FKP on any given day is 0.0000
(5) None of the above.

Question 10

What is the value of the mean and the standard deviation of the number of daily FKP?
(1) µ = 0.2 and σ = 0.4
(2) µ = 0.2 and σ = 0.04
(3) µ = 0.2 and σ = 0.2
(4) µ = 0.4 and σ = 0.4
(5) µ = 0.4 and σ = 0.2

QUESTIONS 6 AND 7 ARE BASED ON THE FOLLOWING INFORMATION.

A Check found that sources of fake news on Facebook are mostly ghost profiles. Suppose
that 20% of profiles on Facebook are ghost profiles. Suppose further that we randomly select 20
Facebook profiles and check whether or not they are ghost profiles.

Question 6

What is the probability that at least 11 profiles are ghost profiles?

(1) 0.0026
(2) 0.0020
(3) 0.0002
(4) 0.0139
(5) None of the above.

Question 7

What is the value of the mean and the standard deviation?

(1) µ = 4 and σ = 3.2
(2) µ = 4 and σ = 1.79
(3) µ = 20 and σ = 1.79
(4) µ = 20 and σ = 3.2
(5) Need more information to determine both values.

QUESTIONS 4, 5 ARE BASED ON THE FOLLOWING INFORMATION.

A Check found that sources of fake news on Facebook are mostly GP. Suppose that 20% of profiles on Facebook are GP. Suppose further that we randomly select 20 Facebook profiles and check whether or not they are GP.

Question 4

Which one of the following statements is incorrect?

(1) The given information describes a binomial experiment with possible outcomes; GP
or not GP.
(2) The number of trials is 20
(3) The 20 trials are independent of each other
(4) The probability of success or GP is 20 trials
(5) The probability of failure or “not GP” is 0.8

Question 5

Which one of the following statements is incorrect?

(1) The probability that all 20 profiles are GP is 0
(2) The probability that no profiles are GP is 0.0115
(3) The probability that only 13 profiles are GP is 0
(4) The probability that only 12 profiles are GP is 0.0001
(5) None of the above

QUESTIONS 1, 2 AND 3 ARE BASED ON THE FOLLOWING INFORMATION.

Around elections time the number of daily fake news posts about politicians follows the following discrete probability distribution.

x 0 1 2 3 4
P (X = x) 0.1 0.15 0.2 0.25 ?

Let X be the number of daily fake news posts.

Question 1

Which one of the following statements is incorrect?

(1) ∑_ P(x) = 1
(2) P(X = 4) = 0
(3) P(X ≤ 4) = 1
(4) P(X ≥ 4) = 0.3
(5) None of the above.

Question 2

What is the expected number of daily fake news posts about politicians around elections time?

(1) 5.3
(2) 4
(3) 2.5
(4) 2.1
(5) 1.3


Question 3

What is the standard deviation of daily fake news posts about politicians around election time?

(1) 1.32
(2) 1.75
(3) 2.5
(4) 1
(5) None of the above

Below is an ordered array of FK. Answer questions 19 to 24.

159 170 172 173 192 193 199 201
201 201 216 217 230 235 256

Q 19
Choose the incorrect
1 Number of observations is 15
2 Sum of all observations is 2759
3 Range is 97
4 Mean is 201

Q 20
Consider
A Median is the 9th observation
B There are 3 modes
C Median is 201
Choose the incorrect
1 A
2 B
3 A, B
4 A, B, C

Q 21
The distribution of FK is
1 Positively skewed.
2 Asymptotic.
3 Asymmetric.
4 Symmetric.

Q 22
Sample standard deviation is
1 25.8
2 26.7
3 374.2
4 666.8

Q 23
Choose the incorrect
1 Q1 position is 4
2 Q2 position is 8
3 Median position is 8
4 Q3 position is 12

Q 24
Choose the incorrect
1 Range is 97
2 Interquartile range is 44
3 Coefficient of variation is 13.3%
4 Range and interquartile range are measures of variation

John wishes to study the mean human body temperature. John organizes a simple random sample which allows him to measure the human body temperature of 45 people at school. His calculations show that his sample has a mean human body temperature of 98.40°F and a standard deviation of 0.62°F. Prior studies indicate that human body temperatures are normally distributed with a standard deviation of 0.50°F. Use the p-value method and a 2% significance level to test the claim that the mean human body temperature of the population is equal to 98.6°F as is commonly believed.

What population parameter is being tested?