Answer:
Part a: P (14/30<x<21/30) = 0.1304
Partb: Expected value= Variance= 0.866
Step-by-step explanation:
The poisson distribution is given by
P(x)= μˣ . e^ -u/ x!
In this question
x= 1
n= 30
μ= 1/30
P(x)= μˣ . e^ -u/ x!
= 0.333. e⁻¹/³⁰/1!
= 0.33*0.967/1
= 0.32208
For 2 weeks
x= 14
n= 30
μ= 14/30
P(x)= μˣ . e^ -u/ x!
= 0.467. e⁻¹⁴/³⁰/14!
= 0.467*0.627/14!
= 0.29285/14!
=3.359*e⁻¹²
= 0.0139
For 3 weeks
x= 21
n= 30
μ= 21/30
P(x)= μˣ . e^ -u/ x!
= 0.7* e⁻²¹/³⁰/21!
= 0.7*0.4965/21!
= 0.3476/21!
=6.8037*e⁻²¹
= 0.11648
Part a:
P (14/30<x<21/30) = P (x= 14/30) + P (x=21/30)
(0.0139 +0.11648) =0.1304
Part b:
Probability of Not receiving the call for two weeks = 1- P (x= 14/30)=0.9861
<u><em>The mean and the variance of the Poisson distribution are equal to μ </em></u>
For x= 14
Expected value not getting wrongly dialed phone call in 2 week = μ= 1-14/30 = 1-0.467= 0.533
Variance of not getting wrongly dialed phone call in 2 week= μ=1- 14/30= 1-0.467= 0.533
Expected value of the additional time until the next wrongly dialed phone call
Expected value not getting wrongly dialed phone call in 2 weeks + Expected value of next wrongly dialed phone call in a month
= 0.533+0.33=0.866
Variance of the additional time until the next wrongly dialed phone call
= Expected value of the additional time until the next wrongly dialed phone call =0.866
18×4=72=4 hats
26-18=8=1 poster
8+8+72=88=4 hats and 2 posters
72=4 hats
72÷4=18= 1 hat costs $18
16÷2=8= 1 poster costs $8
Answer:
y = 9x+80
Step-by-step explanation:
We can use the slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
y = 9x+b
Substitute the point in for x and y
-1 = 9(-9) +b
-1 = -81 +b
Add 81 to each side
-1+81 = b
80 =b
The equation is y = 9x+80
<em>The answer is Ms Hernandez can bring up to 6 people to the zoo.</em>
<em />
<em>x - the number of people that she can bring to the zoo</em>
<em>The parking will cost $7: a = 7</em>
<em>Admission tickets will cost $15.50 per person: b = 15.50x</em>
<em>She can spend on parking and admission tickets $100:</em>
a + b ≤ 100
a = 7
b = 15.50x
7 + 15.50x ≤ 100
15.50x ≤ 100 - 7
15.50x ≤ 93
x ≤ 93 / 15.50
x ≤ 6
