Question

A) A study reports that

36%

of companies in Country A have three or more female board directors. Suppose you select a random sample of 100 respondents.

A) The probability is

68%

that the sample percentage of Country A companies having three or more female board directors will be contained within what symmetrical limits of the population​ percentage?

The probability is

68​%

that the sample percentage will be contained above

nothing​%

and below

nothing​%.

B)An institute reported that

70%

of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members.

B)

The probability is

91%

that the sample percentage will be contained within what symmetrical limits of the population​ percentage?

The probability is

91%

that the sample percentage will be contained above

nothing​%

and below

nothing​%.

C)A marketing survey is conducted in which students are to taste two different brands of soft drink. Their task is to correctly identify the brand tasted. A random sample of

180

students is taken. Assume that the students have no ability to distinguish between the two brands.

C)What is the probability that the sample percentage of correct identifications is greater than

65%?

Answer 1

a)

Mean = 0.36

Standard deviation = sqrt (0.36 * 0.64)/sqrt(100) = 0.048

p ~ N(0.36 , 0.048²)

p^	0.36
n	100
se(p^)	0.048
confidence level	0.68
z	0.994458
lower	0.312266
upper	0.407734

68% lies between (0.3123 , 0.4077)

b)

p^	0.7
n	100
se(p^)	0.045826
confidence level	0.91
z	1.695398
lower	0.622307
upper	0.777693

91% = (0.6223,0.7777)

c)

P(p^ > 0.65)
= P(Z >( 0.65 - 0.5)/sqrt(0.5*0.5/180))
=P(Z> 4.0249)
= 0.0000