Question

Will rate!!

Find the felouring probabilities for the standard normal distribution in R or using the standard normal table, Note 1 always recommend drasing the distribution. (Roand your answers to four decimal places.) "#+ Ex.mple R cede mw-0; sigm a-1; x-x; # Nobe you will have to change the value of x. pnorm(x.mu,sigma) (๑) p(X s 1.61) (b) P(x a 1-61) (c) P(X s -4.33) Find the following percentiles for the standard normal distribution in R or using the stanéard normal table. (Round your ansvers to tire decimal places.) # # Example code mu-01 ซ.gma " i p " p, gnerm(p.mu.sigma) Note you wiE have to change the value of p. 01st (b) 19th c) 74th

Answer 1

#1

a]

$P(x \leq 1.61)$ = 0.9463

Using pnorm( 1.61 , 0 , 1)

b]

$P(x \geq 1.61)$ = $1-P(x \leq 1.61)$    = 1 - 0.9463 = 0.0537

c]

$P(x \leq -4.33)$ = 0.0000 Using pnorm(-4.33 , 0, 1 )

#2

a]

we have p = 1% = 0.01 and find the value of x

x = -2.3263 using qnorm(0.01 , 0, 1)

b]

we have p = 19% = 0.19 and find the value of x

x = -0.8779 using qnorm(0.19 , 0, 1)

c]

we have p = 74% = 0.74 and find the value of x

x = 0.6433 using qnorm(0.74 , 0, 1)