A study reports that 36 % of companies in Country A have three or more female bo
ID: 3049426 • Letter: A
Question
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. Complete parts (a) through (c) below.
a. What is the probability that the sample will have between 34 % and 39 % of companies in Country A that have three or more female board directors? The probability is nothing . (Round to four decimal places as needed.)
b. The probability is 80 % 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 80 % that the sample percentage will be contained above nothing % and below nothing %. (Round to one decimal place as needed.)
c. The probability is 99.7 % 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 99.7 % that the sample percentage will be contained above nothing % and below nothing %. (Round to one decimal place as needed.)
Explanation / Answer
a)
probability that the sample will have between 34 % and 39 % of companies in Country A that have three or more female board directors
b)
for middle 80% ; fall between 10 and 90th percentile for whcih z score =1.2816
hnce correspnding sample % =mean -/+z*std error =29.8% to 42.2%
he probability is 80 % that the sample percentage will be contained above 29.8% and below 42.2%.
c)
as 99.7 % values fall between -/+ 3 std deviation
threfore sample percentage will be contained above 21.60% and below 50.40 %
for normal distribution z score =(p-p)/p here population proportion= p= 0.360 sample size =n= 100 std error of proportion=p=(p*(1-p)/n)= 0.0480Related Questions
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