Question

A random variable X has a normal random varia ble with mean of 20 and standard deviation of 2 (a) Find the two values of X that separates the middle 50% of data (or area) of the distribution of X. Keep at least 2 decimal places (b) Compute the probability that the variable is at most 15. Keep at least 4 decimal places (c) Compute the probability that the variable is less than 12 or more than 21 Keep at least 4 decimal places.

Answer 1

ndmaly and Gven deb-tibuted tandaid duviati that with 240 mean 2 20 at K and X be Suh that, the rC Standand ns mal taky from the o.67f o.67 4 - 0.69) 20 12 (2)-06942+ 20 21. 249 (59 81 21 349 813 Notes: Now con July 18 Mon 30 2 9 16 23 Pobab ili that at most IS Tue 31 3 the Vauiable 10 17 24 Wed 11 18 25 2 Thu 5 12 19 26 Fri 13 20 27 Sat 7 14 21 28 Sun 1 8 15 22 29 n

1S-20 -2.S form the andaid nomal taulay = O.0062 PCzS25 O062 OOO 62 Nlow .considey that the Vatable less than pl72)? prsbabily e than 21 = 12 12-20 2-20 2. Standaid motmal tabl PCZA-T AP(205) P(2-4) + pl770-5) YCX12) tP(7) O 0SS Notes: Plx<i2) + p(x72)- 6 O368 August '18 Hon 6 13 20 27 Tue 7 14 21 28 15 22 29 Wed 1