Answer: 0.965
Step-by-step explanation:
Given : Water use in the summer is normally distributed with
Let X be the random variable that represents the quantity of water required on a particular day.
Z-score :
Now, the probability that a day requires more water than is stored in city reservoirs is given by:-
We can see that on comparing the above value to the given P(X > 350)= 1 - P(Z < b) , we get the value of b is 0.965.
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
Answer:
$5225
Step-by-step explanation:
Use the formula for the amount after simple interest:
"A" is the final amount, or balance.
"P" is the principal, or the starting amount.
"r" is the rate of interest in decimal form.
"t" is the time.
What we know:
P = 5000
t = 3
r = 1.5%
Convert the rate to decimal form by dividing by 100, or moving the decimal place two places to the left.
1.5% => 0.015 = r
Substitute what we know into the formula:
A = P(1 + rt)
A = 5000(1 + (0.015)(3)) <=simplify
A = 5000(1 + 0.045)
A = 5000(1.045)
A = 5225 <= new balance
The new balance of an account is $5225.