Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If
\(P(X>n-3) = \frac{k}{2^n},\)
then k is equal to :
Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If
\(P(X>n-3) = \frac{k}{2^n},\)
then k is equal to :
- 528
- 529
- 629
- 630
The Correct Option is B
Solution and Explanation
The correct answer is (B) : 529
Mean = np = 16
Variance = npq = 8
\(⇒ q = p = \frac{1}{2}\) and \(n = 32\)
\(P(x>n-3) = p(x = n-2) + p(x = n-1) + p(x = n)\)
\(= (^{32}C_2 + ^{32}C_1 + ^{32}C_0). \frac{1}{2^n}\)
\(= \frac{529}{2^n}\)
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Concepts Used:
Statistics
Statistics is a field of mathematics concerned with the study of data collection, data analysis, data interpretation, data presentation, and data organization. Statistics is mainly used to acquire a better understanding of data and to focus on specific applications. Also, Statistics is the process of gathering, assessing, and summarising data in a mathematical form.
Mathematically there are two approaches for analyzing data in statistics that are widely used:
Descriptive Statistics -
Using measures of central tendency and measures of dispersion, the descriptive technique of statistics is utilized to describe the data collected and summarise the data and its attributes.
Inferential Statistics -
This statistical strategy is utilized to produce conclusions from data. Inferential statistics rely on statistical tests on samples to make inferences, and it does so by discovering variations between the two groups. The p-value is calculated and differentiated to the probability of chance() = 0.05. If the p-value is less than or equivalent to, the p-value is considered statistically significant.