Normal Distribution: Mean, Variance, and Standard Deviation

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What is the probability of getting exactly one success in 4 trials if the probability of success is 3/4?

27/64

1/8

81/256

9/32 (correct)

If the probability of getting exactly 2 successes in 5 trials is 0.48, what is the probability of success in each trial?

0.8

0.4 (correct)

0.7

0.6

A fair coin is tossed 5 times. What is the expected number of heads?

4

5

3

2.5 (correct)

If the probability of getting exactly 3 successes in 5 trials is 0.32, what is the probability of getting exactly 2 successes in 5 trials?

0.24 Signup and view all the answers

What is the variance of a binomial distribution with 10 trials and probability of success 0.7?

2.1 Signup and view all the answers

If the probability of getting exactly one success in 4 trials is 0.27, what is the probability of getting exactly 2 successes in 4 trials?

0.48 Signup and view all the answers

What is the percentage of data that falls within 2 standard deviations of the mean in a normal distribution?

95% Signup and view all the answers

What is the formula for the standardized normal probability density function?

1/(2π) * e^(-Z^2/2) Signup and view all the answers

What is the value of the integral of the normal distribution from μ-σ to μ+σ?

0.68 Signup and view all the answers

If a random variable X follows a normal distribution with a mean of μ and a standard deviation of σ, what is the formula for the Z-score?

Z = (X - μ)/σ Signup and view all the answers

What is the percentage of GATE scores that are between 400 and 600, assuming the scores follow a normal distribution with a mean of 500 and a standard deviation of 50?

95% Signup and view all the answers

What is the formula for the variance of a normal distribution?

σ^2 Signup and view all the answers

If the probability of a bomb striking a target is 0.4, what is the probability that exactly 2 out of 6 bombs will strike the target?

0.31104 Signup and view all the answers

In a Poisson distribution, if the probability of getting no misprint in a page of a book is exp(-4), what is the expected value of misprints in a page?

4 Signup and view all the answers

If six coins are tossed 6400 times using a binomial distribution, what is the approximate probability of getting six heads at least 10 times?

0.1053 Signup and view all the answers

In a binomial distribution, if the probability of success is 0.6, what is the probability of at least 2 successes in 5 trials?

0.6630 Signup and view all the answers

If two events A and B are independent, what is the probability of both events occurring?

P(A) × P(B) Signup and view all the answers

If the probability of a page containing more than two misprints is 0.9084, what is the probability of a page containing exactly 2 misprints?

0.1435 Signup and view all the answers