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Sagot :
The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.
Data;
- Mean rate = 0.3
- x = 50
- standard deviation = ?
Poission Rule
Using poission formula,
[tex]P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute[/tex]
Let's substitute the values into the formula.
For 50 calls in 150 hours
For 150 hours = x = 0.3 * 150 = 45
[tex]p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431[/tex]
b)
The probability the next call arrives after 2 hours.
[tex]\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488[/tex]
c)
The number of calls recieved each day is recorded for 50 consecutive days.
for 50 days;
[tex]\lambda = 0.3 * 50 * 24 = 360[/tex]
The mean = 360
The standard deviation is given as
[tex]S.D = \sigma =\sqrt{360} = 18.974\\[/tex]
The probability the sum of these 50 number is less than 356 is
[tex]p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165[/tex]
Learn more on poission formula here;
https://brainly.com/question/7879375
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