GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/18

Question 18 (Textile Engineering & Fibre Science)

If the length of a confidence interval on the mean of a normal distribution with known variance is to be halved, the sample size must

(A)increase by 2 times
(B)decrease by 2 times
(C)increase by 4 times
(D)decrease by 4 times
[Show Answer]

Confidence interval(C.I.) is directly proportional to standard error.

Standard error(S.E.)=\frac{\sigma}{\sqrt n}

Where, n is sample size

\frac{C.I._1}{C.I._2}=\frac{\sqrt n_2}{\sqrt n_1}

Given, C.I._2=\frac{C.I._1}{2}

2=\frac{\sqrt n_2}{\sqrt n_1}

\frac{ n_2}{n_1}=4

n2=4 x n1

Frequently Asked Questions | FAQs

What is the mean of normal distribution?

The mean of a normal distribution is a measure of central tendency and represents the center of the distribution. In a normal distribution, the mean is also the peak of the distribution and is often denoted by the Greek letter μ (mu).
For example, if we have a normal distribution with a mean of 50, it means that the data is centered around 50, and the highest point of the bell-shaped curve is at 50. The mean of a normal distribution is also the expected value or the average value of the random variable that follows this distribution.
In addition, the normal distribution is a symmetric distribution, so the mean is also the median and the mode of the distribution. This means that 50% of the data falls below the mean, and 50% of the data falls above the mean.
The mean of a normal distribution can be calculated using the formula:
μ = (Σx) / n
where μ is the mean, Σx is the sum of all the values in the distribution, and n is the number of values in the distribution. However, in practice, we often use statistical software or calculators to calculate the mean of a normal distribution.

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