Question

Approximately 35.73% of all businesses are owned by women. If you take a sample of 105 businesses in Michigan, what is the probability that less than 32.92% of them would be owned by women?

Question 4 options:

	1) 7.1217
	2) 0.5000
	3) 0.2740
	4) 0.7260
	5) <0.0001

Energetic Co., a battery manufacturer, claims their battery lasts for 67.37 months with a standard deviation of 11.583 months. You randomly sample 16 of these batteries. Assuming the distribution for the battery lifetime is approximately normal, what is the probability the average lifetime is greater than 66.54?

Question 9 options:

	1) 0.8678
	2) 0.4714
	3) 0.6128
	4) 0.3872
	5) 0.5286

Answer 1

Solution:

Question 1)

Given:  

p = 0.3573

n = 105

We have to find:

Find z score:

Thus we get:

Look in z table for z = -0.6 and 0.00 and find area.

P(Z <-0.60)= 0.2743

Thus

From given options 0.2740 is closest to 0.2743

thus correct answer is: 0.2740

Question 2)

Given : ,  

Sample Size = n = 16

We have to find:

Find z score:

Thus we get:

Look in z table for z = -0.2 and 0.09 and find Area.

P( Z< -0.29) = 0.3859

Thus

Thus closest answer is : 0.6128

( Answers are slightly different due to rounding z scores)

To get exact answer use Excel command;

=1-NORM.DIST(x , mean , SE , cumulative )

where x = 66.54

Mean = 67.37

SE = sd / sqrt(n) = 11.583/sqrt(16) =11.583 / 4 = 2.89575

Cumulative = TRUE

Thus we get:

=1-NORM.DIST( 66.54 , 67.37 , 2.89575 , TRUE)

( Copy this excel command and paste it in excel )

=0.6128

Thus correct option is: 0.6128