Question

Question 5 (1 point)

Suppose 65.47% of small businesses experience cash flow problems in their first 5 years. A consultant takes a random sample of 522 businesses that have been opened for 5 years or less. What is the probability that less than 64.62% of the businesses have experienced cash flow problems?

Question 5 options:

	1) 0.6585
	2) <0.0001
	3) 0.3415
	4) 0.5000
	5) 17.6360

Question 6 (1 point)

The rainfall in Aberdeen Reservoir, Washington (the wettest place in the contiguous United States) averages 123.79 inches per year with a standard deviation of 5.958 inches. A random sample of 36 is taken from the population. What is the distribution of the sample mean?

Question 6 options:

	1) Approximately normal with mean 20.6 and standard error 0.99.
	2) 123.79 give or take 5.958.
	3) Approximately normal with mean 123.79 and standard error 0.99.
	4) 68% of sample averages will fall between 117.8 and 129.75.
	5) Approximately normal with mean 123.79 and standard error 5.958.

Question 7 (1 point)

The rainfall in Aberdeen Reservoir, Washington (the wettest place in the contiguous United States) averages 130.78 inches per year with a standard deviation of 6.568 inches. A random sample of 37 is taken from the population. What is the distribution of the sample mean?

Question 7 options:

	1) Approximately normal with mean 130.78 and standard error 6.568.
	2) Approximately normal with mean 130.78 and standard error 1.08.
	3) 130.78 give or take 6.568.
	4) Approximately normal with mean 21.5 and standard error 1.08.
	5) 68% of sample averages will fall between 124.2 and 137.35.

Question 8 (1 point)

Suppose that NBA players average 28.7 points per game with a standard deviation of 8.04. A random sample of 187 players is taken. What is the probability that the sample mean is between 28.48 and 28.7?

Question 8 options:

	1) 0.0109
	2) The sample mean will never fall in this range.
	3) 0.8541
	4) 0.0459
	5) 0.1459

Answer 1

Solution:

5 ) Given that,

n = 522

=65.47% =0.6547

1 - = 1 - 0.6547 = 0.3453

=   = 0.6547

= ( 1 - ) / n

=   0.6547 * 0.3453 / 522

= 0.0208

p (   < 0.6462 )

p ( -    / ) < ( 0.6462- 0.6547 / 0.0208 )

p ( z < -0.0085 / 0.0208 )

Using z table

p ( z < -0.4087 )

= 0.3415

Probability = 0.3415

Option 0.3415 is correct.

6 ) Given that,

mean = = 123.79

standard deviation = = 5.958

n = 36

= 123.79

₌ / n =5.958 36 =0.99

Approximately normal with mean 123.79 and standard error 0.99

7) Given that,

mean = = 130.78

standard deviation = = 6.568

n = 37

=130.78

₌ / n =6.568 37 =1.080

Approximately normal with mean 130.78 and standard error 1.08

8) Given that,

mean = = 28.7

standard deviation = = 8.04

n = 187

= 28.7

₌ / n = 8.04 187 = 0.5879

P (28.48< < 28.7 )

P ( 28.48 - 28.7 /0.5879) < ( - / ) < ( 28.7 - 28.7 / 0.5879)

P (-0.22/ 0.5879< z < 0 / 0.5879 )

P (-0.37 < z < 0)

P ( z < 0) - P ( z < -0.374)

Using z table

= 0.5000- 0.3541

= 0.1459

Probability = 0.1459

Option 0.1459 is correct.