Question

Now assume you have a normal distribution with a mean of 100 and standard deviation of 15 that is composed of 2000 participants. Please answer the following questions,

what is the probability of the following? (please with steps)

a. A score being between 100 and 115

b. A score greater than 130

c. A score less than 70

d. A score either greater than 130 or less than 70

e. A score either greater the 100 or less than 85

Answer 1

a) P(100 < X < 115)

= P(0 < Z < 1)

= P(Z < 1) - P(Z < 0)

= 0.8413 - 0.5

= 0.3413

b) P(X > 130)

= P(Z > 2)

= 1 - P(Z < 2)

= 1 - 0.9772

= 0.0228

c) P(X < 70)

= P(Z < -2)

= 0.0228

d)

= P(Z > 2) + P(Z < -2)

= (1 - P(Z < 2)) + P(Z < -2)

= (1 - 0.9772) + 0.0228

= 0.0228 + 0.0228

= 0.0456

e)

= P(Z > 0) + P(Z < -1)

= (1 - P(Z < 0)) + P(Z < -1)

= (1 - 0.5) + 0.1587

= 0.5 + 0.1587

= 0.6587