What is greater than 0.79 and less than 0.8
2 answers:
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Given:
Length of the ladder = 9.85 m
The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.
To find:
The height to the top and the distance between the wall and the foot of the ladder.
Solution:
let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).
Pythagoras theorem: In a right angle triangle,
In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.
Using the Pythagoras theorem, we get
Here, . Using the quadratic formula, we get
Approximating the value, we get
Distance cannot be negative so
Now we have
Therefore, the base is 4 m and the height is 9 m.
Answer:
a) 0.98% probability that 17 of the 29 people are men.
b) 3.86% probability that the first woman is reached on the 8th call
Step-by-step explanation:
For each person chosen by the agency, there are only two possible outcomes. Either it is a man, or it is a woman. The probability of selecting a man or a women in each trial is independent from other trials. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
(a) What is the probability that 17 of the 29 people are men?
This is P(X = 17) when . So
0.98% probability that 17 of the 29 people are men.
(b) What is the probability that the first woman is reached on the 8th call?
On the first 7 trials, all men, each with a 78% probability.
On the 8th trial, a women, with a 22% probability. So
3.86% probability that the first woman is reached on the 8th call