Problem 17.) Suppose X is a random variable whose sample space is the interval b
ID: 2922124 • Letter: P
Question
Problem 17.) Suppose X is a random variable whose sample space is the interval between 4 and 12 and whose probabilities are determined by the density curve shown to the right. What is P(X 2 10)? 0.2 0.15 0.1 0.05 a. 0.375 b. 0.875 C. 0.125 d. 0.675 3 4 5 6 7 8 9 1011 12 13 Problem 18.) An eclectic musician plays in both a "rock" band and a "country" band. Suppose his weekly income, X, from performances with the rock band has mean $43 with a standard deviation of $21, and his weekly income, Y, from performances with the country band has mean $55 with a standard deviation of $39. Income is thought to be independent between the two bands. The mean difference in income from country band over the rock band is $12. What is the corresponding standard deviation? a. 30.0 b. 32.9 C. 60.0 d. 44.3 Problem 19.) Refer to the setup of the previous problem. If the difference in income between the two bands follows a Normal distribution, what is the probability that in a given week the musician makes more income from performances with the rock band than with the country band a. 0.730 b. 0.270 C. 0.394 d. 0.606Explanation / Answer
17) for probabaility is area under the curve : therefore P(X>10) =(1/2)*(0.125+0.25)*2=0.375
option A is correct
18)corresponding std deviation=(212+392)1/2 =44.3
option d
19)
P(X-Y>0) =P(Z>(0-(43-55)/44.3)=P(Z>0.2709)=0.394
option C is correct