Question

In: Statistics and Probability

Let x be a continuous random variable that follows a distribution skewed to the left with...

Let x be a continuous random variable that follows a distribution skewed to the left with ?= 92 and ?=15. Assuming n/N <= .05, find the probability that the sample mean, x bar, for a random sample of 62 taken from this population will be (ROUND ANSWERS TO FOUR DECIMAL PLACES):

a) less than 81.5

P(less that 81.5)=

b) greater than 89.7

P(greater than 89.7)=

Please show your work.

Solutions

Expert Solution

Solution :

Given that ,

mean = = 92

standard deviation = = 15

n = 62

= = 92

= / n = 15 / 62 = 1.9050

a ) P( < 81.5) = P(( - ) / < (81.5-92) /1.9050 )

= P(z < -5.51) =0

probability = 0.0000

b ) P( > 89.7 ) = 1 - P( < 89.7 )

= 1 - P[( - ) / < (89.7-92) /1.9050 ]

= 1 - P(z <-1.21 )

= 1- 0.1131 = 0.8869

probability = 0.8869


Related Solutions

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...
A random variable X follows the continuous uniform distribution with a lower bound of ?8 and...
A random variable X follows the continuous uniform distribution with a lower bound of ?8 and an upper bound of 11. a. What is the height of the density function f(x)? (Round your answer to 4 decimal places.)   f(x)    b. What are the mean and the standard deviation for the distribution? (Round your answers to 2 decimal places.)   Mean      Standard deviation    c. Calculate P(X ? ?6). (Round intermediate calculations to 4 decimal places and final answer to...
2] Let x be a continuous random variable that has a normal distribution with μ =...
2] Let x be a continuous random variable that has a normal distribution with μ = 48 and σ = 8 . Assuming n N ≤ 0.05 , find the probability that the sample mean, x ¯ , for a random sample of 16 taken from this population will be between 49.64 and 52.60 . Round your answer to four decimal places.
Let x be a continuous random variable that has a normal distribution with μ = 60...
Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n ≤ 0.05N, where n = sample size and N = population size, find the probability that the sample mean, x¯, for a random sample of 24 taken from this population will be between 54.91 and 61.79. Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n...
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)?
Let X be a continuous random variable that has a uniform distribution between 0 and 2...
Let X be a continuous random variable that has a uniform distribution between 0 and 2 and let the cumulative distribution function F(x) = 0.5x if x is between 0 and 2 and let F(x) = 0 if x is not between 0 and 2. Compute 1. the probability that X is between 1.4 and 1.8 2. the probability that X is less than 1.2 3. the probability that X is more than 0.8 4. the expected value of X...
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.
Let be a continuous random variable that has a normal distribution with μ = 48 and...
Let be a continuous random variable that has a normal distribution with μ = 48 and σ = 8. Assuming , n/N ≤ 0.05, find the probability that the sample mean, x , for a random sample of 16 taken from this population will be more than 45.30 . Round your answer to four decimal places.
Let the continuous random variable X have probability density function f(x) and cumulative distribution function F(x)....
Let the continuous random variable X have probability density function f(x) and cumulative distribution function F(x). Explain the following issues using diagram (Graphs) a) Relationship between f(x) and F(x) for a continuous variable, b) explaining how a uniform random variable can be used to simulate X via the cumulative distribution function of X, or c) explaining the effect of transformation on a discrete and/or continuous random variable
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT