* mens heights are normally distributed with mean of 69.5 in. and standard devia
ID: 3178004 • Letter: #
Question
* mens heights are normally distributed with mean of 69.5 in. and standard deviation 2.4 in
* women's heights are normally distributed with mean 63.8 in. and standard deviation 2.6 in.
23 most of the live characters at Disney World have height requirements with a minimum of 4ft 8in and a maximum of 6ft 3in.
a0 find the percentage of women meeting the height requirement
b find the percentage of men metting the height requirement
if the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women what are the new height requirements?
23- section two
*the gulfstream 100 is an executive jet that seats sex, and it has a doorway height of 51.6in.
D)what percentage of adult men can fit through the door without bending?
e) what percentage of adult women can fit through the door without bending?
F) does the door design with a height of 51.6 in appear to be adequate?
G) what doorway height would allow 60% of men to fit without bending?
SECTION THREE
25) when a water taxi sank in baltimore inner harbor an investigation revealed that the safe passenger load for the water taxi as 3500 lb. It was also noted that the mean weight of a passangers was assumed to be 140 lb. assume a worst case scenario in which all of the passengers are adult men. assume that weights of men are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8lb.
A) if one man is randomly selected find the probability that he weighs less than 174lb
b) with a load limit of 3500 lb how many male passengers are allowed if we assume a mean of 140lb?
C) with a load limit of 3500 lb how many male passengers are allowed if we use a new mean weight of 182.9 lb?
D) why is it necessary to periodically review and revise the number of passengers that are allowed to board?
Explanation / Answer
1.
1ft = 12 inch
Men mean height = 69.5
Men stdev height = 2.4
Women mean height = 63.8
Women stdev height = 2.6
Disney has 4.8 to 6ft3
a. P( women meeting req of Disney height)
P(4.8<X<6.3)
= P( (4.8*12-63.8)/2.6*12 <Z< 6.3*12-63.8 / 2.6*12)
=P(-.2<Z<.38)
=.6480-.4207
=.2273
b. Same exerxise for men:
P(4.8<X<6.3)
=P(-.4<X<.22)
= .5871-.3446
= .2425
c. Exclude only tallest 5% men and shortest 5% women
= 63.8 - 1.645*2.4 = 59.852
and 69.5 - 1.645*2.6 = 65.223
These are the new limits of height
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