wsw11-Graded_Assignment_Sep_2025_Statistics_I_Qualifier (2)

Graded Assignment - (Sep 2025 - Statistics I - Qualifier)

The due date for submitting this assignment has passed. Due on 2025-12-10, 23:59 IST. You may submit any number of times before the due date. The final submission will be considered for grading.

Last Submitted: You have last submitted on: 2025-12-10, 07:16 IST

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Question 1

A match predictor claims that he can predict the result of a match correctly 75% of the time. It is agreed that his claim will be accepted if he correctly predicts the results of at least 6 of 7 matches. What is the probability that his claim gets rejected?

• ${\sum }_{i=1}^5$ ${}^7{C}_i\times (0.75{)}^i\times (0.25{)}^{7-i}$
• ${\sum }_{i=0}^5$ ${}^7{C}_i\times (0.75{)}^i\times (0.25{)}^{7-i}$
• ${\sum }_{i=0}^6$ ${}^7{C}_i\times (0.75{)}^i\times (0.25{)}^{7-i}$
• ${\sum }_{i=1}^6{}^7{C}_i\times (0.75{)}^i\times (0.25{)}^{7-i}$

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• ${\sum }_{i=0}^5$ ${}^7{C}_i\times (0.75{)}^i\times (0.25{)}^{7-i}$

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Question 2

If $X\sim Binomial(n,p)$, then which of the following statement/s is/are always true? ($n>0$ and $0<p<1$)

• $E(X)\le Var(X)$
• $E(X)<Var(X)$
• $E(X)\ge Var(X)$
• $E(X)>Var(X)$
• $Var(X)\le S.D(X)$
• $Var(X)\ge S.D(X)$

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• $E(X)>Var(X)$

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Question 3

Two friends (say '$A$' and '$B$') could not decide whether to play a racing game or a boxing game on Xbox. They decide to play a card-game first. If '$A$' wins at least 3 rounds out of the 4 rounds of the card game played, then the boxing game will be played. The chances of '$A$' winning in any round of the card game is 4:5. Find the probability that the boxing game will be played on Xbox? (Enter the answer correct to 2 decimal places)
Hint: If the chances of happening of an event is x:y then, the probability equals $\frac{x}{x+y}$ Your Answer: 0.23

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.2,0.26

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Question 4

Let $X$~ Binomial(6,p). If the probabilities of 4 and 5 successes are approximately 0.2882 and, 0.3651 respectively, then find the parameter ‘p’ of the distribution.(Enter the answer correct to 2 decimal places) Your Answer: 0.76

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.73,0.79

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Question 5

If the expected number of sixes hit by a batsman on $n$ balls is 6.39 and the variance for the same is 1.8531, then what is the probability of him hitting at least one six on any randomly selected $n$ balls? Assume that the probability of him hitting a six on any ball is constant. (Enter the answer correct to 4 decimal places) Your Answer: 1.0000

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.9995,1

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Question 6

The probability of a student clearing a competitive exam is $\frac{1}{5}$. If he gives the exam 7 times, then what is the probability of him clearing the exam at least twice?(Enter the answer correct to 2 decimal places) Your Answer: 0.42

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.39,0.45

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Question 7

Choose the correct condition/s about binomial distribution.

• The probability of success $p$ keeps varying for each trial.
• The number of trials $n$ is finite.
• The trials are dependent on each other.
• The trials are independent of each other.

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• The number of trials $n$ is finite.
• The trials are independent of each other.

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Question 8

Rithika wants to test whether the coin she has is a fair coin or not. To test this, she conducted an experiment of tossing the coin 5 times. Binomial random variable $X$ is defined as the total number of heads($i$) after 5 tosses. The probability distribution of the binomial random variable is given in Table 11.1.G.

$X=i$

$P(X=i)$

0

0.00243

1

0.02835

2

0.1323

3

0.3087

4

0.36015

5

0.16807

Table 11.1.G: Binomial Distribution

What is the approximate probability of getting a head in tossing the given coin? (Enter the answer correct to one decimal place) Your Answer: 0.7

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) 0.7

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Question 9

At a school function, It is noticed that 9% of the students are not wearing polished shoes and 12% of students are not wearing school ties. It is announced that the students who have committed any of the infractions will be punished, and that these two infractions are independent of one another. If a teacher selects 5 students at random, then find the probability that exactly three of the students will be punished for any of the infractions?

• ${}^5{C}_3(0.1992{)}^3(0.8008{)}^2$
• ${}^5{C}_3(0.0108{)}^3(0.9892{)}^2$
• ${}^5{C}_3(0.09{)}^3(0.91{)}^2+{}^5{C}_3(0.12{)}^3(0.88{)}^2$
• ${}^5{C}_3(0.21{)}^3(0.79{)}^2$

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• ${}^5{C}_3(0.1992{)}^3(0.8008{)}^2$

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Question 10

There are 10 black and 16 blue pens in a box. A pen is chosen at random, and its colour is noted. If the process repeats independently, 12 times with replacement, then calculate the expected number of black pens chosen?

• $\frac{120}{26}$
• $\frac{192}{26}$
• $\frac{72}{16}$
• $\frac{120}{16}$

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• $\frac{120}{26}$

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Question 11

Number of calls received at an office follows a Poisson distribution with an average of 1 call per minute. Find the probability that no call will be received in two minutes at the office. (Enter the answer correct to 2 decimal accuracy.) Your Answer: 0.14

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.10,0.16

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Question 12

Calculate $P(X=2)$. (Enter the answer correct to 2 decimal places) Your Answer: 0.50

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.47,0.53

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Question 13

Calculate the value of $E(X)$. (Enter the answer correct to 2 decimal places) Your Answer: 1.80

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 1.77,1.83

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Question 14

What is the probability that exactly 2 blue balls are selected? Enter the answer correct to two decimal places. Your Answer: 0.42

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.39,0.45

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Question 15

What is the expected number of blue balls selected in the draw? Enter the answer correct to two decimal places. Your Answer: 2.29

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 2.26,2.32

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Question 16

Identify the distribution of $X$.

• $X\sim$Binomial$(5,0.6)$
• $X\sim$Binomial$(5,0.4)$
• $X\sim$Bernoulli$(0.6)$
• $X\sim$Bernoulli$(0.4)$

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• $X\sim$Binomial$(5,0.4)$

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Question 17

What is the probability that at most one of the product passes the quality control inspection? Enter the answer correct to three decimal places. Your Answer: 0.337

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.334,0.340

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