Normal Distribution properties
Trending Questions
- 0.2881
- 0.5762
- 0.8181
- 0.1616
Let X1, X2 and X3 be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probability P(X1+X2≤X3) is the largest} is
- 0.16
What term refers to the standard deviation of the sampling distribution?
What is a normal probability curve?
- 1.2
- 0.5
- greater than zero and less than 0.5
- greater than 0.5 and less than 1.0
- 1.0
Let X be a zero mean unit variance Gaussian random variable. E[|X|] is equal to
- 0.7978
- <50%
- 50%
- 75%
- 100%
(Area under standard normal curve between z = 0 and z = 0.6 is 0.2257; and between z = 0 and z = 1.0 is 0.3413)
- 36
- 23
- 12
- 10
- 1√2π
- 2√2√π
- 2√2π
- 2√π
- 1−2α
- 1−α
- 1−α/2
- 2α
F(XN)=11+exp(−1.7255XN|XN|0.12), where XN= standard normal deviate. If mean and standard deviation of annual precipitation are 102 cm and 27 cm respectively, the probability that the annual precipitation will be between 90 cm and 102 cm is
- 66.7%
- 50.0%
- 33.3%
- 16.7%
A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders, who maintain an average daily balance more than Rs. 500 is ______.
- 50
Which one of the given measures of dispersion is considered best?
Standard deviation
Range
Mean deviation
Coefficient of variation
- 0.1517
- 0.1867
- 0.2666
- 0.3646
- 0
- 0.5
- 1
- 10σ
- 49
- 12
- 23
- 59
The area (in percentage) under standard normal distribution curve of random variable Z within limits from -3 to +3 is _____.
- 99.7
Let X be a Gaussian random variable mean 0 and variance σ2. Let Y = max(X, 0) where max (a, b) is the maximum of a and b. Th emedian of Y is
- 0
- Y is normally distributed with mean 0 and variance 1
- Y is normally distributed with mean 0 and variance 5
- Y has mean 0 and variance 5, but is NOT normally distributed
- Y has mean 0 and variance 1, but is NOT normally distributed
- 1
- 0.5
- π
- π/2
For a construction project the mean and standard deviation of the completion time are 200 days and 6.1 days respectively. Assume normal distribution and use the value of standard normal deviate z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be
- 210
What is a standard normal probability distribution?
fx(x)=1√8πe−⎧⎪ ⎪⎨⎪ ⎪⎩(x−1)28⎫⎪ ⎪⎬⎪ ⎪⎭, −∞<x<∞
Then ∫∞1fx(x)dx?
- 0
- 12
- 1−1e
- 1
What is the role of sample size in the central limit theorem?
- CkT
- √kTC
- kTC
- √kTC
What is the difference between standard error and standard deviation?
- 0.0125
- 0.025
- 0.05
- None of these
- 0.067
- 0.073
- 0.082
- 0.091
A function f(x) is designed as to be a valid probability density function the value of A must be
f(x)=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩0;x<31A(3x+5) ;3<x<6. Forf(x)0;x>6
- 55.5
- 40.5
- 50
- 63.5