Question

Given a standard normal distribution, find the area under the curve which
lies
(i) to the left of z = 1.43;
(ii) to the right of z = -0.89;
(iii) between z = -2.16 and z = -0.65.

Given a standard normal distribution, find the value of k such that
(i) P(Z < k) = 0.0427
(ii) P(Z > k) = 0.2946
(iii) P(-0.93 < Z < k) = 0.7235

Answer 1

NOTE:

Finding the area under standard normal distribution curve is equivalent to finding the corresponding probability.

1.

Probability of type P(Z < k) is calculated in R using command

pnorm(k, 0, 1, lower.tail = TRUE)

and

Probability of type P(Z > k) is calculated in R using command

pnorm(k, 0, 1, lower.tail = FALSE)

2.

The value of k for probability of type P(Z < k) = p is calculated in R using command

qnorm(p, 0, 1, lower.tail = TRUE)

You can also find these probabilities and values of k from a standard normal distribution table.