Question

X follows a normal distribution with mu = 4.7 and sigma = 1.1.

P(3.05 < X < 3.93) to four decimal places is:

	1) 0.6752
	2) 0.1752
	3) 0.3248
	4) 0.8248

Answer 1

Probability of normal distribution can be done through the standard normal distribution

Z =(X - µ)/σ

Given

sigma,σ = 1.1

mu,µ = 4.7

P(3.05<X<3.93)

= P[(3.05-4.7)/1.1 <Z<(3.93-4.7)/1.1 ]

= P(-1.65/1.1 < Z< -0.77/1.1)

= P(-1.5 < Z <-0.7)

= 0.2420 - 0.0668

= 0.1752

From standard normal distribution table we get the values of Z

Z (-1.5) = 0.0668

Z (-0.7) = 0.2420