According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical, civil, and industrial) were women. Suppose a random sample of 50 engineers is selected. How likely is it that the random sample of 50 engineers will contain 8 or more women in these positions?
0.1612
0.1020
0.0314
0.0821
Solution
random sample = 50
% of engineers (electrical, mechanical, civil, and industrial) who were women p = 10.5
Sample proportion phat >= 8/50
phat >= 0.16
Std error = sqrt[p * (1 - p)/n] = sqrt[0.105 * (1 - 0.105)/50] = 0.043
probability that the random sample of 50 engineers will contain 8 or more women in these positions is given by 1 - P[Z = (phat - p)/std error]
= 1 - P[Z = (0.16 - 0.105)/0.043]
= 1 - P[Z = 1.27]
= 1 - 0.898 = 0.1020
.
According to the most recent Labor Department data- 10-5- of engineers.docx
1. According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical,
civil, and industrial) were women. Suppose a random sample of 50 engineers is selected. How
likely is it that the random sample of 50 engineers will contain 8 or more women in these
positions?
0.1612
0.1020
0.0314
0.0821
Solution
random sample = 50
% of engineers (electrical, mechanical, civil, and industrial) who were women p = 10.5
Sample proportion phat >= 8/50
phat >= 0.16
Std error = sqrt[p * (1 - p)/n] = sqrt[0.105 * (1 - 0.105)/50] = 0.043
probability that the random sample of 50 engineers will contain 8 or more women in these
positions is given by 1 - P[Z = (phat - p)/std error]
= 1 - P[Z = (0.16 - 0.105)/0.043]
= 1 - P[Z = 1.27]
= 1 - 0.898 = 0.1020
![According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical,
civil, and industrial) were women. Suppose a random sample of 50 engineers is selected. How
likely is it that the random sample of 50 engineers will contain 8 or more women in these
positions?
0.1612
0.1020
0.0314
0.0821
Solution
random sample = 50
% of engineers (electrical, mechanical, civil, and industrial) who were women p = 10.5
Sample proportion phat >= 8/50
phat >= 0.16
Std error = sqrt[p * (1 - p)/n] = sqrt[0.105 * (1 - 0.105)/50] = 0.043
probability that the random sample of 50 engineers will contain 8 or more women in these
positions is given by 1 - P[Z = (phat - p)/std error]
= 1 - P[Z = (0.16 - 0.105)/0.043]
= 1 - P[Z = 1.27]
= 1 - 0.898 = 0.1020](https://image.slidesharecdn.com/accordingtothemostrecentlabordepartmentdata-10-5-ofengineers-230128035316-c0a4faa5/85/According-to-the-most-recent-Labor-Department-data-10-5-of-engineers-docx-1-320.jpg)
