Question

A study reports that % of companies in Country A have three or more female board directors. Suppose you select a random sample of 100 respondents. Complete parts (a) through (c) below. 36 a. What is the probability that the sample will have between % and % of companies in Country A that have three or more female board directors? 29 40 The probability is . (Round to four decimal places as needed.) b. The probability is % 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? 60 The probability is 60 % that the sample percentage will be contained above % and below %. (Round to one decimal place as needed.) c. The probability is % 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? 95 The probability is 95 % that the sample percentage will be contained above % and below %. (Round to one decimal place as needed.)

Answer 1

p=0.36

n=100

For p,

Mean = 0.36

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

p ~ N(0.36 , 0.048²)

What is the probability that the sample will have between 33​% and 37​% of companies in Country A that have three or more female board​ directors(four decimal places)

P (0.33 < p < 0.37)

= P(-0.625 < Z < 0.208333)

= P(Z < 0.208333) - P(Z < -0.625)

= 0.5825 - 0.2660

= 0.3165 Answer

The probability is 70​% 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? (one decimal place)

The 70% symmetric limits are

The probability is 95% 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? (one decimal place)

The 95% symmetric limits are