Question

In: Statistics and Probability

? is a normal random variable with µ = 2 and σ = 5. Find the...

? is a normal random variable with µ = 2 and σ = 5. Find the value of c such that ?{|?−3|>?}=0.7

Solutions

Expert Solution

Give

Since Normal distribution is symmetric therefore

From statistical table and R software

Comparing both above probabilities


Related Solutions

If a variable is Normal (µ = 10, σ = 1.2) to. Find the probability that...
If a variable is Normal (µ = 10, σ = 1.2) to. Find the probability that X is between 10 and 12. (10 points) b. Calculate the X corresponding to the 80% percentile (10 points) c. Find the probability that X is greater than 9 (10 points) d. If a sample of 15 data is taken, calculate the probability that the average is between 9.2 and 10. (10 points) and. Calculate the 90% percentile of the average of X if...
Given a normal distribution with µ = 10 and σ = 2, find (a) the normal...
Given a normal distribution with µ = 10 and σ = 2, find (a) the normal curve area to the right of x = 6; (b) the normal curve area between x = 6 and x = 14; (c) the two values of x that contain the middle 75% of the normal curve area. please show all work if possible. Thank you
Let Z be a normal random variable with mean µ = 0 and standard deviation σ...
Let Z be a normal random variable with mean µ = 0 and standard deviation σ = 1, that is, Z ∼ N(0, 1). Find each of the following: (a) P(Z ≤ −1.13). (b) P(Z ≥ −2.18). (c) P(2.13 ≤ Z ≤ 2.57). (d) P(−2.3 ≤ Z ≤ −1.1). (e) P(0 ≤ Z ≤ 1.54). (f) P(−1.54 ≤ Z ≤ 1.54). (g) N(1.1243). (h) N(−1.1243).
For a normal random variable, with  μ = 19, and  σ = 6, find the following...
For a normal random variable, with  μ = 19, and  σ = 6, find the following probabilities. (a) Pr(X  ≤  32.2) (b) Pr(X  >  4.00)
Suppose X is a normal random variable with μ = 600 and σ = 89. Find...
Suppose X is a normal random variable with μ = 600 and σ = 89. Find the values of the following probabilities. (Round your answers to four decimal places.) (a) P(X < 700) (b) P(X > 350) (c) P(300 < X < 900)
Suppose X is a normal random variable with μ = 350 and σ = 40. Find...
Suppose X is a normal random variable with μ = 350 and σ = 40. Find the values of the following probabilities. (Round your answers to four decimal places.) (a) P(X < 468) (b) P(390 < X < 454) (c) P(X > 390)
For normal data with unknown mean µ and σ^2, we use the prior f (µ, log(σ))...
For normal data with unknown mean µ and σ^2, we use the prior f (µ, log(σ)) = 1. 23 data points: 5.36 5.29 5.58 5.65 5.57 5.53 5.62 5.29 5.44 5.34 5.79 5.1 5.27 5.39 5.42 5.47 5.63 5.34 5.46 5.3 5.75 5.68 5.85 Q. Draw sample (or theoretical) posterior joint pdf of (µ, σ^2), marginal pdf of µ, marginal pdf of σ^2, and posterior predictive pdf.
Question 1 Given a normal distribution with µ=15 and σ = 5, what is the probability...
Question 1 Given a normal distribution with µ=15 and σ = 5, what is the probability that X>20 X<20 X<20 or X>20 INSTRUCTIONS: Show all your work as to how you have reached your answer. Please don’t simply state the results. Show graphs where necessary.
For a normal distribution with a mean of µ = 150 and an SD of σ...
For a normal distribution with a mean of µ = 150 and an SD of σ = 15: 3. Find these probabilities: a. p (X > 150) b. p(X < 120) c. p(X < 170) d. p(130 < X < 175) A researcher wants to test her hypothesis that drinking caffeine while learning a new skill will aid in developing that skill. In order to test her hypotheses, she recruits a sample of 25 beginner piano students from a nearby...
Part A: Suppose a random variable X have mean of µ and standard deviation σ. Let...
Part A: Suppose a random variable X have mean of µ and standard deviation σ. Let a and b be constants. i) Derive the expected value of aX + b. ii) Derive standard deviation of aX + b Part B: Suppose that in country A, the price of certain good has a mean of $100 and a variance of 25, in A-dollars. Country B has a fixed exchange rate with A so that it takes 2 B-dollars to buy 1...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT