Question

1. A sample of n = 16 scores is obtained from a population with µ = 50 and σ = 16. If the sample mean is M = 58, then what is the z-score for the sample mean?

   		z = - 2.00
   		z = +0.50
   		z = +2.00
   		z = +8.00

2. A researcher selects a random score from a normally distributed population. What is the probability that the score will be greater than z = +1.5 and less than z = -1.5?

   		.07
   		.13
   		.43
   		.86

3. Finn receives a final exam score of 65. The class had a mean of 75 and standard deviation of 10. What percent of students in Finn's class scored lower than him?

   		84%
   		50%
   		34%
   		16%

4. A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 95 from this distribution?

   		p = 0.9332
   		p = 0.1587
   		p = 0.4332
   		p = 0.0668

Answer 1

Solution:

1)

z-score for the sample mean

= [M - ]/[/n]

= [58 - 50]/[16/16]

= +2.00

z = +2.00

2)

P(Z < -1.5 OR Z > 1.5)

= 1 - { P(Between -1.5 AND 1.5) }

= 1 - { P(Z < 1.5) - P(Z < -1.5) }

= 1 - { 0.9332 - 0.0668 }

= 0.13

Answer : 0.13

3)

Given, X follows Normal distribution with,

   = 75

= 10

Find P(X < 65)

= P[(X - )/ <  (65 - )/]

= P[Z <  (65 - 75)/10]

= P[Z < -1.00]

= 0.1587 ... ( use z table)

= 15.87%

= 16%

Answer : 16%

4)

Given, X follows Normal distribution with,

   = 80

= 10

P(X > 95)

= P[(X - )/ >  (95 - )/]

= P[Z > (95 - 80)/10]

= P[Z > 1.50]

= 1 - P[Z < 1.50]

= 1 - 0.9332 ..( use z table)

=  0.0668

Answer : 0.0668