Question

The score on Math 206 class X, is normally distributed with μ=74.5 and σ=8.7.

Assume for the sake of this problem that the score is a continuous variable.

(a) Write the event ''a score equal to 64.5'' in terms of X:  .

(b) Find the probability of this event:

(c) Find the probability that a randomly chosen score is greater than 84.5:  .

(d) Find the probability that a randomly chosen score is between 64.5 and 84.5:  .

Answer 1

µ = 74.5, σ = 8.7

a) Event, X = 64.5

b) P(X = 64.5) =

= P( (X-µ)/σ = (64.5-74.5)/8.7 )

= P(z = -1.1494)

Using excel function:

= NORM.S.DIST(-1.1494, 1)

= 0.1252

c) P(X > 84.5) =

= P( (X-µ)/σ > (84.5-74.5)/8.7)

= P(z > 1.1494)

= 1 - P(z < 1.1494)

Using excel function:

= 1 - NORM.S.DIST(1.1494, 1)

= 0.1252

d) P(64.5 < X < 84.5) =

= P( (64.5-74.5)/8.7 < (X-µ)/σ < (84.5-74.5)/8.7 )

= P(-1.1494 < z < 1.1494)

= P(z < 1.1494) - P(z < -1.1494)

Using excel function:

= NORM.S.DIST(1.1494, 1) - NORM.S.DIST(-1.1494, 1)

= 0.7496