Question

In: Statistics and Probability

A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17....

A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17. Find the probability associated with each of the following intervals. (Round your answers to four decimal places.)

(a)    

1.00 < x < 1.20




(b)    

x > 1.37




(c)    

1.35 < x < 1.50

Solutions

Expert Solution

Solution :

Given that ,

mean = = 1.6

standard deviation = = 0.17

(a)

P(1.00 < x < 1.20) = P((1.00 - 1.6 / 0.17) < (x - ) / < (1.20 - 1.6) / 0.17) )

P(1.00 < x < 1.20) = P(-3.53 < z < -2.35)

P(1.00 < x < 1.20) = P(z < -2.35) - P(z < -3.53) = 0.0094 - 0.0002 = 0.0092

Probability = 0.0092

(b)

P(x > 1.37) = 1 - P(x < 1.37)

= 1 - P((x - ) / < (1.37 - 1.6) / 0.17)

= 1 - P(z < -1.35)

= 1 - 0.0885

= 0.9115

P(x > 1.37) = 0.9115

Probability = 0.9115

(c)

P(1.35 < x < 1.50) = P((1.35 - 1.6 / 0.17) < (x - ) / < (1.50 - 1.6) / 0.17) )

P(1.35 < x < 1.50) =  P(-1.47 < z < -0.59)

P(1.35 < x < 1.50) =  P(z < -0.59) - P(z < -1.47) = 0.2776 - 0.0708 = 0.2068

Probability = 0.2068


Related Solutions

A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17....
A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17. Find the probability associated with each of the following intervals. (Round your answers to four decimal places.) (a)     1.00 < x < 1.30 (b)     x > 1.32 (c)     1.25 < x < 1.50
Given that x is a Normal random variable with a mean of 10 and standard deviation...
Given that x is a Normal random variable with a mean of 10 and standard deviation of 4, find the following probabilities: (6 points) P(x<6.7) P(x>12.5) P(8.8<x<12.5)
A normal random variable x has mean μ = 1.8 and standard deviation σ = 0.18....
A normal random variable x has mean μ = 1.8 and standard deviation σ = 0.18. Find the probabilities of these X-values. (Round your answers to four decimal places.) (a)     1.00 < X < 1.50 (b)     X > 1.39 (c)     1.45 < X < 1.60
1) A normal random variable x has an unknown mean μ and standard deviation σ =...
1) A normal random variable x has an unknown mean μ and standard deviation σ = 2. If the probability that x exceeds 4.6 is 0.8023, find μ. (Round your answer to one decimal place.) μ = 2) Answer the question for a normal random variable x with mean μ and standard deviation σ specified below. (Round your answer to four decimal places.) μ = 1.3 and σ = 0.19. Find P(1.50 < x < 1.71). P(1.50 < x <...
Suppose that X is a Normal random variable with mean 1.2 and standard deviation 0.5. a....
Suppose that X is a Normal random variable with mean 1.2 and standard deviation 0.5. a. Find a value a such that P(X?a)=0.10. b. Find a value b such that P(X?b)=0.10. c. Find a value c such that P(1.2?c<X<1.2+c)=0.30.
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
Let x be a normal random variable with mean 35 and standard deviation 2. a. Find...
Let x be a normal random variable with mean 35 and standard deviation 2. a. Find P(30 < x < 38). .9270 b. Find P(x > 34). .6915 c. Find P(x = 36). 0 d. Find the area under the distribution of x to the left of 31. .0228
A. A normal random variable has an unknown mean μ and a standard deviation σ =...
A. A normal random variable has an unknown mean μ and a standard deviation σ = 2. If the probability that x exceeds 6.5 is .9732; find μ. B. A standard normal random variable has μ = 0 and a standard deviation σ = 1. Find the probability of less than -2.73. C. A standard normal random variable has μ = 0 and a standard deviation σ = 1. Find the probability greater than 3.28. D. A standard normal random...
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.
1) Consider X a normal random variable with mean 4 and standard deviation 2. Given that...
1) Consider X a normal random variable with mean 4 and standard deviation 2. Given that P(X<6)=0.841345 , compute P(2<= x <= 6) 2)Consider X a normal random variable with mean 10 and standard deviation 4. Given that P(x>9)=0.598708 and P(x<12)=0.691464 . Compute P(8< x < 11).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT