Question

A study about strategies for competing in the global marketplace states that 52% of the respondents agreed that companies need to make direct investments in foreign countries. It also states that about 70% of those responding agree that it is attractive to have a joint venture to increase global competitiveness. Suppose CEOs of 95 manufacturing companies are randomly contacted about global strategies.

(a) What is the probability that between 44 and 52 (inclusive) CEOs agree that companies should make direct investments in foreign countries?
(b) What is the probability that more than 56 CEOs agree with that assertion?
(c) What is the probability that fewer than 60 CEOs agree that it is attractive to have a joint venture to increase global competitiveness?
(d) What is the probability that between 55 and 62 (inclusive) CEOs agree with that assertion?

Answer 1

here mean =np=95*0.52=49.4

and strd deviaiton =sqrt(np(1-p))=4.8695

as z score =(X-mean)/std deviaiton

a)probability that between 44 and 52 (inclusive) CEOs agree =P(44<=X<=52)

=P((43.5-49.4)/4.8695<Z<(52.5-49.4)/4.8695)=P(-1.21<Z<0.64)=0.7389-0.1131 =0.6258

b)P( more than 56 CEOs agree)=P(X>56)=P(Z>(56.5-49.4)/4.8695)=P(Z>1.46)=0.0721

c)

P(X<60)=P(Z<(59.5-49.4)/4.8695)=P(Z<2.07)=0.9808

d)

P(55<=X<=62)=P((54.5-49.4)/4.8695<Z<(62.5-49.4)/4.8695)=P(1.05<Z<2.69)=0.9964-0.8531 =0.1433