Normal Distribution: Mean, Variance, and Standard Deviation
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Questions and Answers

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?

    <p>0.24</p> Signup and view all the answers

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

    <p>2.1</p> 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?

    <p>0.48</p> 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?

    <p>95%</p> Signup and view all the answers

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

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

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

    <p>0.68</p> 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?

    <p>Z = (X - μ)/σ</p> 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?

    <p>95%</p> Signup and view all the answers

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

    <p>σ^2</p> 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?

    <p>0.31104</p> 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?

    <p>4</p> 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?

    <p>0.1053</p> 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?

    <p>0.6630</p> Signup and view all the answers

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

    <p>P(A) × P(B)</p> 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?

    <p>0.1435</p> Signup and view all the answers

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