Question

1. A sample size of 49 drawn from a population with a mean of 36 and a standard deviation of 15 for the size of an English class. What is the probability the class will have greater than 40

a. .9693

b. .4693

c. .0808

d. .0307

2. A sample size of 49 drawn from a population with a mean of 36 and a standard deviation of 15 for the size of an English class. What is the probability the class will was between 30 and 40?

a. .0363

b. .4693

c. .9667

d. .1608

3. The expected value (the average of all possible samples of a gin size) of the sample mean is expected to be equal to the mean of the population from which the random samples are taken.

a. true

b. false

Answer 1

Solution :

Given that,

mean = = 36

standard deviation = = 15

n = 49

= = 36

= / n = 15 / 49 = 2.14

1) P( > 40) = 1 - P( < 40)

= 1 - P[( - ) / < (40 - 36) /2.14 ]

= 1 - P(z < 1.87)

Using z table,    

= 1 - 0.9693

= 0.0307

2) P(30 < < 40)  

= P[(30 - 36) / 2.14 < ( - ) / < (40 - 36) / 2.14 )]

= P(-2.80 < Z < 1.87)

= P(Z < 1.87) - P(Z < -2.80)

Using z table,  

= 0.9693 - 0.0026  

= 0.9667

3) True