Suppose that 90 % of people are right-handed. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $X$ be the number of right-handed people in a sample of $n = 10$. The probability of a person being right-handed is $p = 0.9$,and the probabil

Vedclass · Accepted Answer

$\sum_{r=0}^{6} {^{10}C_r} (0.9)^r (0.1)^{10-r}$

Vedclass · Answer

(B) Let $X$ be the number of right-handed people in a sample of $n = 10$. The probability of a person being right-handed is $p = 0.9$,and the probability of being left-handed is $q = 1 - 0.9 = 0.1$. $X$ follows a binomial distribution $B(n, p) = B(10, 0.9)$. The probability that at most $6$ people are right-handed is $P(X \le 6)$. Using the probability mass function of the binomial distribution,$P(X = r) = {^{n}C_r} p^r q^{n-r}$. Thus,$P(X \le 6) = \sum_{r=0}^{6} {^{10}C_r} (0.9)^r (0.1)^{10-r}$.

Suppose that $90 \%$ of people are right-handed. What is the probability that at most $6$ of a random sample of $10$ people are right-handed?

Similar Questions

$A$ coin is tossed $n$ times. If the probability of getting $6$ heads is equal to the probability of getting $8$ heads,then find the value of $n$.

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. The mean of the number of queens is:

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. What is the probability that out of $5$ such bulbs,none will fuse after $150$ days of use?

$A$ fair coin is tossed $15$ times. The probability that the tail will appear at least thrice is

Let $X$ be a random variable having a Binomial distribution $B(7, p)$. If $P(X=3) = 5 P(X=4)$,then the variance of $X$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module