Question

Please may I have help with this question. thank you

6. Find the area under the standard normal curve for each. b. Between 0 and 1. 96 a. Between -1.20 and 1.50

Answer 1

The area between a and b is given by: -

P(a<zb)= (b) D(a)

P(za)D(a

P(z> a) 1- P(<a) 1 - (a

here, is the cdf of standard normal distribution. The calculations are done in R. On R.H.S is output and on L.H.S.is code.

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RR Console R Untitled R Editor #Between -1.2 and l.5 > pnorm (1.5, mean 0, sd 1) -pnorm (-l.2, mean = 0, sd 1) [ 0.8181231 #Between -1.2 and 1.5 1)-pnorm (-1.2, mean = 0, sd 1) sd Between and .9e 0, sd 1) -pnorm (0, mean 0, sd 1) pnorm (1.96, mean 0, sd 1)-pnorm (0, mean 0, sd 1) #Between -2.43 and -0.95 11 0.4750021 pnorm(-0.95, mean - 0, sd-l)-pnorm(-2,43, mean -0, sd- 1) #Between -2.43 and -0.95 pnorm (-0.95, mean 0, sd 1)-pnorm (-2.43, mean-0, sd - 1) mean o sd 1)-pnorm (1.12, mean 0, sd 1) To the left of 1.75 .12 and 1.98 0, sd 1) pnorm (1.75, mean > pnorm (1.98, mean = 0, sd 1)-pnorm (l.12, mean =0, sd 1) [ 0.1075051 To the left of 1.75 To the left of 1.77 sd 1) To the riaht of 2.04 mean = 0, sd 1) ni o.9599408 #To the left of 1. 77 > pnorm (1. 77, mean-0, sd 1) [1] 0.9616364 To the right of 2.04 1-pnorm (2.04, mean 0, sd 1) To the right of -0.89 1-pnorm(-0.89, mean 0, sd 1) mean 0, sd 1) O 02067516 > To the right of -0.89 -pnorm (-0.89, mean 1 0.0132671 0, sd 1)