i already did it , but i want to make sure my answers are correct , will give positive feedback but i need GOOD handwriting if by hand ! thank you sooo much love u

MATH-251 Probability and Statistics, RIT, 2228 1. Let X be a continuous r mariable with probability density function (x) = artha for 0 > = 1 - 8 doe = 1( 3 - 3 ) : 3 segment to the longer segment. E ( ' = ) = E (x - 1) In x - x 10.5 6- 1 - 14 ( 0 .5 ) + 0 - - ( + In ( 0.5) ( TAX ) = E ( 1 + 2 ) = It it doc = ( se - In ( 1 - x) ) 0 .5 - 14 ( 0. 5 ) E ( m ) = - 0.5 + in( as ) + 1 + In (..5 ) = 0.5 + In (1) = 0'S E ( " ) = 0.5 MATH-251 Probability and Statistics, RIT, 2228 S. In a given high school distributed with a mean of 2.9 and (a) What is the approximate pe se of students in this high school with GPA between 2.3 and 3.5? X2N ( 2.4 ) ..675 P ( 2.3 LX L 3. 5) P ( : 2 1 ) L26 ( 2 8 - 2 0 ) P ( - 1 2 2 6 1 ) 2 x P ( O L z L 1 ) 2* 0.3413 = 0.6826 = 68.26% (b) What is the approximate low highest 5% of the students? P (x z x0 ) = 0.05 20 = 1. 645 2 , - 2.9 = 1. 645 20 = 2. 4 + 1. 645 x 0.6 20 = 3.882 MATH-251 Probability and Statistics, RIT, 2228 4. Suppose that the a 10 minutes. entially distributed with mean value (a) What is the probability that a customer will spend more than 15 minutes in the bank? anE ( + . ) fx ( x ) = (# * 2. P ( x 2 15 5 = S Palx ) cha = fire " che = ( /15 = - 1 6 0 - ( * ) . ( " / 2 (b) What is the probability that a customer will spend more than 15 minute assume that he is spending more than 10 minutes in the bank minutes (total) in the bank, if we P ( x 7 15 / 2 7 10 ) = P (x 710 + 5 / x 2 10 ) Is -1/2 - 1 / 2 = -1 (0 -e = er