Maya chatted online with all her friends for 2/3 of an hour on Saturday and 1/4 of an hour on sunday. During that time period, s
2 answers:
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Answer: (a) Percentage of 25 year old men that are above 6 feet 2 inches is 11.5%.
(b) Percentage of 25 year old men in the 6 footer club that are above 6 feet 5 inches are 2.4%.
Step-by-step explanation:
Given that,
Height (in inches) of a 25 year old man is a normal random variable with mean and variance
.
To find: (a) What percentage of 25 year old men are 6 feet, 2 inches tall
(b) What percentage of 25 year old men in the 6 footer club are over 6 feet. 5 inches.
Now,
(a) To calculate the percentage of men, we have to calculate the probability
P[Height of a 25 year old man is over 6 feet 2 inches]= P[X>]
P[X>74] = P[ >
]
= P[Z > 1.2]
= 1 - P[Z ≤ 1.2]
= 1 - Ф (1.2)
= 1 - 0.8849
= 0.1151
Thus, percentage of 25 year old men that are above 6 feet 2 inches is 11.5%.
(b) P[Height of 25 year old man is above 6 feet 5 inches gives that he is above 6 feet] = P[X,
- X,
]
P[X >
I X >
] = P[X > 77 I X > 72]
=
=
=
=
=
=
= 0.024
Thus, Percentage of 25 year old men in the 6 footer club that are above 6 feet 5 inches are 2.4%.
Given:
Eighteen 2.5 gallon buckets are needed to fill a cistern with water.
To find:
The constant of variation.
Solution:
If y is directly proportional to x, then
Where, k is constant of variation.
In the given problem, water in cistern (w) is directly proportional to number of buckets (n).
(Capacity of each bucket is 2.5 gallons)
Therefore, the constant of variation is 2.5.