Question

8. Suppose XN(100,52). Find P(95 < X < 110). 9. Suppose X is a normal random variables with parameters x = 10 and o2 = 36. Compute (a) P(X > 5) and geometrically sketch what you have found. (b) P(4 < X < 16) and geometrically sketch what you have found. (c) P(X < 8) and geometrically sketch what you have found.

Answer 1

2 2 Here it is given that Xu N (190, 52 Hi the know that if Xu Nl Mio 2) Z-*=# and we x100 un(UI) a PE 01/10) Plosc X Clou) IŠ the L X-100 X-180 stolu 5 5 F PE ( 26 -2 § (-2) - & (-3 where I y -3 calf of z

= 0.0228 - 0:0013 ܫܐܘ ܝܘ ܦܐܠܐܒ II C XL/Uu) 20.0215 9 Hine it is given that XUNC LU, 36) Hit 2 theri Z = X-10 unlo, ) t 9) 5-10 6 6 PLx75E PL X-10 Pris | P(x>!)= 0.2023 0.8333 0:7977 to X

Here P(x>5 =0.7977 that means Curre under area of the Normal XS M0.7977 6 b) R645X Slu) = f[4-10 < x-10 (10-10 6 - =P[16 22o 02-511) 0:5 -0.158.7 (4% X510) XCIU) I 013413 2 Х x 4 40 here P(4 L XLlu) - 0.34 13 that means area under the normal come under the condition 46x<10 is 0.3413

의 P(XL 8) = xo ( 81o 6 =pZC-0333) P(XLG) 03494 6. (0, that means ?(x②) 2. 0394 area under the normal curve with XL8 %3694 2