Question

In: Statistics and Probability

If X represents a random variable coming from a normal distribution with mean 3 and if...

If X represents a random variable coming from a normal distribution with mean 3 and if P(X>4.2)=0.36P(X>4.2)=0.36, then P(3<X<4.2)=0.14P(3<X<4.2)=0.14.

  • ___True
  • ___False

Solutions

Expert Solution

P(3<X<4.2)= P(X<4.2) - P(X<3)

=1-P(X>4.2) - 0.5

=1- 0.36 - 0.5

= 0.14

Ans : TRUE                                                                                                                                       

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Given a random variable X following normal distribution with mean of -3 and standard deviation of...
Given a random variable X following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5 is also normal. (1)Find the distribution of Y, i.e. μy,σy (2)Find the probabilities P(−4<X<0),P(−1<Y<0) (3)Find the probabilities P(−4<X¯<0),P(3<Y¯<4) (4)Find the 53th percentile of the distribution of X
The random variable X follows a normal distribution with a mean of 10 and a standard...
The random variable X follows a normal distribution with a mean of 10 and a standard deviation of 3. 1. What is P(7≤X≤13)? Include 4 decimal places in your answer. 2. What is the value of k such that P(X>k)=0.43? Include 2 decimal places in your answer.
Let the random variable X follow a normal distribution with a mean of μ and a...
Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ. Let 1 be the mean of a sample of 36 observations randomly chosen from this population, and 2 be the mean of a sample of 25 observations randomly chosen from the same population. a) How are 1 and 2 distributed? Write down the form of the density function and the corresponding parameters. b) Evaluate the statement: ?(?−0.2?< ?̅1 < ?+0.2?)<?(?−0.2?<...
Random variable X is drawn from a normal distribution with mean 5.44 and std dev 2.54....
Random variable X is drawn from a normal distribution with mean 5.44 and std dev 2.54. Calculate the probability of X being less than 3.29. What is the probability of X exceeding 4.61? What is the probability of X lying between 5.79 and 7.8? Verify your answers to parts 1 2 and 3 above using numerical sampling.
Random variable X is drawn from a normal distribution with mean 13.59 and standard deviation 2.39....
Random variable X is drawn from a normal distribution with mean 13.59 and standard deviation 2.39. Calculate the probability of X being less than 11.31. What is the probability of X exceeding 12.52? What is the probability of X lying between 13.75 and 15.09? Verify your answers to parts 1 and 2 above using numerical sampling. (Harder) verify your answers to part 3 above using numerical sampling.
Let X be a continuous random variable following normal distribution with mean value of: (a is...
Let X be a continuous random variable following normal distribution with mean value of: (a is 1) and standard deviation of b is 1/10 ,  What is the mode of X? (1 mark)  What is median of X? (1 mark)  What is ?(? > ?)? (1mark)  What is ?(? − ? < ? < ? + ?)? (1 mark)  What is ?(? − 1.96? < ? < ? + 1.96?))? (1mark)
Let X be a continuous random variable following normal distribution with mean value of: (a is...
Let X be a continuous random variable following normal distribution with mean value of: (a is the last digit of your student number) and standard deviation of b (b is the last digit of your student number divided by 10), a=9 b=9/10 What is the mode of X? What is median of X? What is P(X>a)? What is P(a-b<X<a+b)? What is P(a-1.96b<X<a+1.96b)?
1) Let   x be a continuous random variable that follows a normal distribution with a mean...
1) Let   x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41. (a) Find the value of   x > 321 so that the area under the normal curve from 321 to x is 0.2224. Round your answer to the nearest integer. The value of   x is_______ (b) Find the value of x so that the area under the normal curve to the right of x is 0.3745. Round...
Let X be a continuous random variable having a normal probability distribution with mean µ =...
Let X be a continuous random variable having a normal probability distribution with mean µ = 210 and standard deviation σ = 15. (a) Draw a sketch of the density function of X. (b) Find a value x∗ which cuts left tail of area 0.25 . (c) Find a value y∗ which cuts right tail of area 0.30. (d) Find a and b such that p(a ≤ X ≤ b) = 0.78.
Given a random variable XX following normal distribution with mean of -3 and standard deviation of...
Given a random variable XX following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5Y=0.4X+5 is also normal. (1)(2pts) Find the distribution of YY, i.e. μY,σY.μY,σY. (2)(3pts) Find the probabilities P(−4<X<0),P(−1<Y<0).P(−4<X<0),P(−1<Y<0). (3)(3pts) Find the probabilities P(−4<X¯<0),P(3<Y¯<4).P(−4<X¯<0),P(3<Y¯<4). (4)(4pts) Find the 53th percentile of the distribution of X.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT