Statistics for Data Science I End Term: 13 April 2025, Set QDD3 (January 2025 term)

Consider the following statements related to permutation and combination. Which of the following is/are true?

A surveyor collects data on the electricity bills of 100 randomly selected households in a particular month. Which of the following statements about this data is/are correct?

A customer support center tracks the time agents take to resolve customer queries. Let X (in minutes) represent the resolution time, which follows an exponential distribution with an average resolution time of 2 minutes. Which of the following option(s) is/are true?

A group of 7 people (A, B, C, D, E, F, G) is to be seated in a row for a photograph.
The following conditions must be satisfied:
• A and B must always sit next to each other.
• D and E cannot sit next to each other.
What is the total number of valid arrangements under these conditions?

At a university, 60% of the students are enrolled in science programs, while 40% are enrolled in arts programs. Among science students, 25% participate in research projects, whereas 15% of arts students participate in research project. If a student is chosen at random, what is the probability that he/she participates in a research project? Enter the answer correct to two decimal places.

The total number of observations in a dataset is 8. If the mean of first 4 observations is 12 and the mean of all 8 observations is 18, then find the mean of last 4 observations.

A shopping mall conducted a survey among 150 customers to study the relationship between age group and preferred payment method (Cash or Digital). The collected data is shown in the table Q.1:

Based on the above data, answer the given subquestions.

What proportion of the total customers prefer digital payments? Enter the answer correct to two decimal places.

A shopping mall conducted a survey among 150 customers to study the relationship between age group and preferred payment method (Cash or Digital). The collected data is shown in the table Q.1:

Based on the above data, answer the given subquestions.

How many customers of age between 18 to 45 prefer cash payment?

The probability mass function of a discrete random variable X is given by,

Based on the above data, answer the given subquestions.

Find the value of E(6X − 2).

The probability mass function of a discrete random variable X is given by,

Based on the above data, answer the given subquestions.

Find the value of V (3X − 4).

Let X represent the time a student takes to complete a test, which follows a uniform distribution between 45 and 75 minutes. Using this information, answer the given subquestions.

Let X represent the time a student takes to complete a test, which follows a uniform distribution between 45 and 75 minutes. Using this information, answer the given subquestions.

Given that a student has already spent 60 minutes on the test, what is the probability that they will take more than 65 minutes to complete it?

A small game involves spinning a wheel that has an equal chance of landing on one of four colors: Red, Blue, Green, or Yellow. Let the random variable X represent the number of times the wheel lands on Red in three independent spins.
Based on the above data, answer the given subquestions.

Find probability that the wheel lands on red exactly 2 times out of the three spins.

A small game involves spinning a wheel that has an equal chance of landing on one of four colors: Red, Blue, Green, or Yellow. Let the random variable X represent the number of times the wheel lands on Red in three independent spins.
Based on the above data, answer the given subquestions.

Find the value of E(X). Enter the answer correct to two decimal places.