Question

Consider the following statements with respect to probability distributions :
A. When mean (μ) = 1 and standard deviation (σ) = 0 for a data set, normal distribution is called standard normal distribution.
B. In a normal distribution of data, z is given by \(z=\frac{\mu-x}{\sigma}\)
C. P('t' success) is the (r + 1)^th term in the binomial expansion of (q + p)ⁿ.
D. In a random experiment, a collection of trials is called Bernoulli, if trials are department by nature.
E. When a random variable whose value is obtained by measuring and it takes many values between two values, it is called a continuous random variable.
Choose the correct answer from the options given below :

• A. C and E only
• B. A and B only
• C. B and C only
• D. C and D only

Answer 1

The Correct Option is A

To solve the problem, we need to analyze each statement related to probability distributions and verify their correctness:

A. When mean (μ) = 1 and standard deviation (σ) = 0 for a data set, normal distribution is called standard normal distribution.
This statement is false. A standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.

B. In a normal distribution of data, z is given by \(z=\frac{\mu-x}{\sigma}\)
This statement is false. The correct formula for the z-score in a normal distribution is \(z=\frac{x-\mu}{\sigma}\), not \(z=\frac{\mu-x}{\sigma}\).

C. P('t' success) is the (r + 1)^th term in the binomial expansion of (q + p)ⁿ.
This statement is true. In a binomial distribution, the probability of 'r' successes in 'n' trials is given by the (r+1)^th term in the expansion of (q + p)ⁿ, where q = 1-p.

D. In a random experiment, a collection of trials is called Bernoulli, if trials are department by nature.
This statement is false. In a Bernoulli trial, there are only two possible outcomes and each trial is independent, not "department by nature."

E. When a random variable whose value is obtained by measuring and it takes many values between two values, it is called a continuous random variable.
This statement is true. A continuous random variable can take an infinite number of values within a given range.

Based on the analysis, the correct answer is: C and E only.