please solve it carefully 4. It was rumored that Britain\'s domestic intel- lige
ID: 2884441 • Letter: P
Question
please solve it carefully
4. It was rumored that Britain's domestic intel- ligence service MI5 has an upper limit on the height of its spies, on the assumption chat tall people stand out (although MIS denies it). The rumor said that, to apply to be a spy, you can be no taller than 5 feet 11 inches (180.3 cm) if you are a man, and no taller than 5 feet 8 inches (172.7 cm) if you are a woman (supposedly to allow the spies to blend in with a crowd) a. If the mean height of British men is 177.0 cm, with standard deviation 7.1 cm, what proportion of British men would be precluded from being spies b this height follows a normal distribution. hypothetical height restriction? Assume that b. The mean height of women in Britain is 163.3 crm, with standard deviation 6.4 cm. Assuming a normal distribution of female height, what fraction of women meet the height standard for application to MIS? c. Sean Connery, the original James Bond in the movies, is about 183.4 cm tall. By how many standard deviations does he exceed the height limit for spies?Explanation / Answer
Uppr limit is 180.3 for men
Upper limit is 172.7 for women
Mean = 177
SD = 7.1
x = 180.3
So, z = (x - mean)/SD
z = (180.3 - 177)/7.1
z = 0.46478873239436619718309859154929577464788732394
We basically need P(z < 0.4647887323943662)
which is 0.6772
So, the number excluded is
1 - 0.6772
0.3228
32.28% excluded
--------------------------------------------------
b)
SD = 6.4
Mean = 163.3
x = 172.7
z = (172.7 - 163.3)/6.4
z = 1.46875
We need P(z < 1.46875)
0.9292
So, 92.92% of women will be able to be spies
---------------------------------------------------
c)
x = 183.4
Ht limit for men = 180.3
SD = 7.1
(183.4 - 180.3)/7.1
0.4366197
So, approx 0.4366 standard deviations
above the mean height
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.