Question

For a continuous random variable XX, the population mean and standard deviation are 118 and 11, respectively. A sample of 42 observations is randomly selected. The mean of the sampling distribution of x¯ is:

• 118
• 1.18
• 1.7
• 11

For the standard normal distribution, the area between z=-1.58 and z=1.57is:

• 0.9418
• 0.9936
• 0.0014
• 0.8847

For the standard normal distribution, the area to the left of z=-1.06 is:

• 0.0082
• 0.1446
• 0.8554
• 0.0764

Answer 1

Solution :

Given that ,

(A)mean = = 118

standard deviation = = 11

n = 42

sample distribution of sample mean is ,

=

=118

(B)

P(-1.58 < Z <1.57 )

= P(Z < 1.57) - P(Z < -1.58)

Using z table,  

=   0.9418-0.0571

area=0.8847

(C)P(z < -1.06)

Using z table  

=0.1446

area =0.1446