Find the area under the standard normal distribution curve to the left of z = 2.09.

round(pnorm(2.09), 4)

Find the area under the standard normal distribution curve to the right of z = -1.14.

round(pnorm(-1.14, lower.tail = FALSE), 4)

Find the area under the standard normal distribution curve between z = -1.62 and z = 1.35.

round(pnorm(1.35), 4) - round(pnorm(-1.62), 4)

Find the probability for each.

1. P(0 < z < 2.53) 2. P(z < 1.73) 3. P(z > 1.98)

round(pnorm(2.53), 4) - round(pnorm(0), 4)
round(pnorm(1.73), 4)
round(pnorm(1.98, lower.tail = FALSE), 4)

Find the z value such that the area under the standard normal distribution curve between 0 and the z value is 0.2123. (Sol: 0.56).

round(qnorm(0.7123), 2)

## Extra Practice Set

Find the area under the curve:

Between z = 0 and z = 0.98

# P (Z <= 0) = 0.5
pnorm(0)

# P (Z <= 0.95)
pnorm(0.98)

round((pnorm(0.98) - pnorm(0)), 4)

Between z = 1.23 and z = 1.90

round((pnorm(1.90) - pnorm(1.23)), 4)

To the left of z = -2.15 and to the right of z = 1.62

round((pnorm(-2.15) + pnorm(1.62, lower.tail = FALSE)), 4)

P(-0.20 < z < 1.56)

round((pnorm(1.56) - pnorm(-0.20)), 4)

Find the z value to the right of the mean so that 69.85% of the area under the distribution curve lies to the left of it.

round(qnorm(0.6985), 4)

Find two z values so that 48% of the middle area is bounded by them.

round((qnorm(0.74)), 4)

Find P(-1 < z < 1), P(-2 < z < 2), and P(-3 < z <3).

(round(pnorm(1), 4) - 0.5) * 2

(round(pnorm(2), 4) - 0.5) * 2

(round(pnorm(3), 4) - 0.5) * 2