Question

If a normal distribution has a mean of 323.15 and standard deviation of 112.28, what is P(x≤216.98)?

If a normal distribution has a mean of 343.11 and standard deviation of 110.24, what is P(x>216.98)?

If a normal distribution has a mean of 14.5 and standard deviation of 4.6 what is P(x≤20)?

If a normal distribution has a mean of 14.5 and standard deviation of 4.6, what is P(x≥13)?

For a standard normal distribution with mean of 0 and standard deviation of 1, what is P(x≤0.48)?

For a standard normal distribution with mean of 0 and standard deviation of 1, what is P(-0.34≤x≤0.48)?

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

1) Mean = 323.15

Standard deviation = 112.28

P(X 216.98) = P(Z < (216.98 - 323.15)/112.28)

= P(Z < -0.95)

= 0.1711

2) Mean = 343.11

Standard deviation = 110.24

P(X > 216.98) = 1 - P(X < 216.98)

= 1 - P(Z < (216.98 - 343.11)/110.24)

= 1 - P(Z < -1.14)

= 1 - 0.1271

= 0.8729

3) Mean = 14.5

Standard deviation = 4.6

P(X 20) = P(Z < (20 - 14.5)/4.6)

= P(Z < 1.20)

= 0.8849

4) Mean = 14.5

Standard deviation = 4.6

P(X 13) = 1 - P(X < 13)

= 1 - P(Z < (13 - 14.5)/4.6)

= 1 - P(Z < -0.33)

= 1 - 0.3707

= 0.6293

5) P(X 0.48) P(Z < 0.48)

= 0.6844

6) P(-0.34 X 0.48) = P(Z < 0.48) - P(Z < -0.34)

= 0.6844 - 0.3669

= 0.3175