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Tems11 [23]
3 years ago
9

Emergency 911 calls to a small municipality in Idaho come in at the rate of one every two minutes. Assume that the number of 911

calls is a random variable that can be described by the Poisson distribution.
(a) What is the expected number of 911 calls in one hour? per hour
(b) What is the probability of three 911 calls in five minutes? If required, round your answer to four decimal places.
(c) What is the probability of no 911 calls during a five-minute period? If required, round your answer to four decimal places.
Mathematics
1 answer:
nordsb [41]3 years ago
4 0

Answer: a) 30, b) 0.2138, c) 0.0820

Step-by-step explanation:

Since we have given that

X be the number of calls in 1 hour = 60 minutes

Rate of one call every two minutes.

\lambda=\dfrac{1}{2}

(a) What is the expected number of 911 calls in one hour?

\lambda=\dfrac{1}{2}\times 60=30

(b) What is the probability of three 911 calls in five minutes? If required, round your answer to four decimal places.

\lambda=\dfrac{1}{2}\times 5=2.5

Number of calls = 3

So, P(X=3) is given by

P(X=3)=\dfrac{e^{-\lambda}\lambda^x}{x!}\\\\P(X=3)=\dfrac{e^{-2.5}\times (2.5)^3}{3!}\\\\P(X=3)=0.2138

(c) What is the probability of no 911 calls during a five-minute period? If required, round your answer to four decimal places.

P(X=0)=\dfrac{e^{-2.5}(2.5)^0}{0!}=0.0820

Hence, a) 30, b) 0.2138, c) 0.0820

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The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives an
Mashcka [7]

Answer:

Step-by-step explanation:

To calculate ;

1) the expected value of the job satisfaction score for senior executives ;

expected value = Summation (Px)

= 1 x 0.05 + 2 x 0.09 + 3 x 0.03 + 4 x 0.42 + 5 x 0.41

= 4.05

2) the expected value of the job satisfaction score for middle managers;

= 1 x 0.04 + 2 x 0.10 + 3 x 0.12 + 4 x 0.46 + 5 x 0.28

= 3.84

c) the variance of job satisfaction scores for executives and middle managers (to 2 decimals).

Executives ; Variance = Summation(PX^2 - Summation(PX)^2

i) For Executive Managers = 1 x 0.05 + 2^2 x 0.09 + 3^2 x 0.03 + 4^2 x 0.42 + 5^2 x 0.41 - 4.05^2 = 1.246 = 1.25

ii) for middle managers ; 1 x 0.04 + 2^2 x 0.10 + 3^2 x 0.12 + 4^2 x 0.46 + 5^2 x 0.28 - 3.84^2 = 1.134 = 1.13

d) the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals). Executives, Middle managers;

For Executives = square root [ 1 x 0.05 + 2^2 x 0.09 + 3^2 x 0.03 + 4^2 x 0.42 + 5^2 x 0.41 - 4.05^2] = 1.12

For Middle Managers ; Square root [1 x 0.04 + 2^2 x 0.10 + 3^2 x 0.12 + 4^2 x 0.46 + 5^2 x 0.28 - 3.84^2 ] = 1.06

e) from the values gotten for the variance of both executive and middle managers, the variance of the former is more than that of the latter as such higher satisfaction with the executive managers.

5 0
3 years ago
What is thirty two percent of fifty six
mojhsa [17]

Answer: 17.92

Step-by-step explanation:

32% of 56  

Change to fraction

32 /100 x 56

Change to decimal

0.32 x 56

= 17.92

5 0
3 years ago
When the family arrived in New Delhi from Rome, the youngest son asked the pilot how fast he was flying the plane. The pilot tol
Elden [556K]

Answer:

7 hours

Step-by-step explanation:

It is given that the plane was flying at 847 km/hour. So the speed of the plane was 847 kilometers per hour.

It is also given that the distance between Rome and New Delhi is 5,929 kilometers.

We know that the distance is equal to the product of speed and time, so we have,

d= s\times t, where 'd' represents the distance, 's' represents the speed, and 't' represents the time.

Putting the values we get,

5929= 847 \times t

Solving for 't' we get,

t= \frac{5929}{847}=7

So the time taken to fly from Rome to New Delhi is 7 hours.

7 0
3 years ago
A TV that usually sells for $186.67 is on sale for 20% off. If sales tax on the TV is 8%, what is the price of the TV, including
Furkat [3]

Answer:

$161.28288  or $161.28 if rounded

Step-by-step explanation:

first find 10% of the original cost

186.67/10 =18.667

18.667 x 2 = 37.334 (20%)

186.67 - 37.334 = 149.336

to find the tax, mulitple 149.336 x 1.08

1.08 because, 100% of the cost, plus 8% of the cost for tax

= 161.28288

5 0
3 years ago
Point A is at (-1,-9) and Point M is at (0.5,-2.5).
leva [86]
  • Midpoint Formula: (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})

So firstly, let's start with the x-coordinates. Since we know the midpoint's x-coordinate and point A's x-coordinate, we can solve for point B's x-coordinate as such:

\frac{-1+x}{2}=0.5\\\\-1+x=1\\\\x=2

Next, do the same thing except solve for the y-coordinate and using point A's y-coordinate and the midpoint's y-coordinate:

\frac{-9+y}{2}=-2.5\\\\-9+y=-5\\\\y=4

<u>Putting it together, point B's coordinates are (2,4).</u>

4 0
2 years ago
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