Answer:
Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.
Step-by-step explanation:
The formula for the probability of an exponential distribution is:
P(x < b) = 1 - e^(b/3)
Using the complement rule, we can determine the probability of a customer having to wait more than 10 minutes, by:
p = P(x > 10)
= 1 - P(x < 10)
= 1 - (1 - e^(-10/10) )
= e⁻¹
= 0.3679
The z-score is the difference in sample size and the population mean, divided by the standard deviation:
z = (p' - p) / √[p(1 - p) / n]
= (0.5 - 0.3679) / √[0.3679(1 - 0.3679) / 100)]
= 2.7393
Therefore, using the probability table, you find that the corresponding probability is:
P(p' ≥ 0.5) = P(z > 2.7393)
<em>P(p' ≥ 0.5) = 0.0031</em>
<em></em>
Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.
It’s 5 1/3 because 16 divided by 3 is 5 1/3
Susanne is 16 years old.
b = Bob's age
s = Susanne's age
d = Dakota's age
Bob's age is 4 times greater than Susanne's age:
b = 4s
Dakota is three years younger than Susanne:
d = s - 3
The sum of Bob's, Susanne's, and Dakota's ages is 93:
b + s + d = 93
solve these equations:
b = 4s
d = s - 3
b + s + d = 93
and get:
b = 64 years
s = 16 years
(remember that s = Susanne)
d = 13 years
