Question

Check my work 4 Let y = ex where X is normally distributed with u = 3.6 and o=0.9. Compute the following values. [You may find it useful to reference the z table.) a. Compute RY s 10.4). (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) 14.28 points P(Y S 10.4) eBook Hint Print References b. Compute P8.9 <Y<10.1). (Leave no cells blank - be certain to enter "0" wherever required. Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) P(8.9 <Y < 10.1) c. Compute the 90th percentile of Y. (Round your intermediate calculations to at least 4 decimal places, "z" value to 3 decimal places, and final.answer to the nearest whole number.)

Answer 1

Here it is ginen that y = ex where with х is normally distributed mean (m) -3.6 and SD) = 0.9 Xu N[3.6, (0.9?] and we know that if Xu NCH, o 2) then Za X-M No,1) d since Here xu N[3.6 (0.9) 2] so z= x-3.6 UN(0, 1) o.g a) Pl y a 10.4) = Plex c 10.4) = P(x < ln (10.4) ) P(xs 2.3418)

JI 20b] 0 -3.6 2.3418-306 org . -1.398 +19353] =P[24 o 9735 0.084 IPEYE Y E io. 41 70.935 0.0 Bil

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c ) goth percentill percentill off can be cal culated as PLY 59] = 90 0.90 100 P ot cy] =0.90 PC x < lny] =0.90 P(x-316 ceny -3.6 lny -3.6 7 = 0.90 0.9 0.9 Now t5 eny-3.6 oig Prze 090 3.632 how using standard normal fable we know that 12c 1.282] = 0.90 on comparing this to abune we at en y-3.6 1.282 og

eny= 2: 6+ С.9x 292 Ди9 — 4:15 3 (73 — е 9 -- |16.02.43 goth percentily