Question

If continuous random variable X~ N(6,4), compute 1) Probability P(X>6.) 2) Probability P(3.<X<7.) 3) Probability P(-1.5 <X<2.5) 4) Probability P(-2.<X – 2<5.) Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.

Answer 1

If continous random variable y me N(6,4) compute Probability Prze?,6) 스 (x-3) 4 ( 1') z = we know that o here M = 6 f Os2 Be-N PP27,5) = 6 - ? =P(27,0) a Now use 2 score table ! - 0.5

(s.1-32 Jd (5.072) d = (5.0 > ? 5 s.ro )da 2 G+ <2< 9-E =P( 9 [hoto > z> H-E Jd = A>*5&ld Probability all

Find out this Area -1.5 0.5 0.6915- <1-0.93 32 0.9332] = 0.6247 0.6915 -0.0668 P(-1.5 * <2.5) Probability call ㅑ PI61.5-M) <2< (2.5 - u) line

9-5.1- ) d = 2.5-6 C 2 < bisa ८ = p [-3.75 <2<7.75) Find out P[241-75) – Pr23-3.75] C Areas 츠 -3.75 4.75 0 = 21-P[2<175}} - KI-P(Z < 3.45]} >

11-0.95993 < - 0.4444 } 0.0401 = 0.00000.001 = 0.0400 € Probability P (-2 s 2-2 2-2<5) - we can write this as, P(-2+2 saasta) =pCo Et<7) Jo << 7-4 0

0 6 엘 225 ] PC-3 42 <os] 2 = r2 <o.s] - f[24-3] [z<o] - I-P[z]) 11 6. 641S - 〈I- 0.49 1- 0.49 3+} 0.6902 Find Area ㅠ 0 05 - 3

## for all problems above use

normal approximation of : z = ( x - mean ) / standard deviation follow standard normal distribution and

use z score table for all .