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 = ?

<h3>Poission Rule</h3>

Using poission formula,

$P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute$

Let's substitute the values into the formula.

For 50 calls in 150 hours

For 150 hours = x = 0.3 * 150 = 45

$p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431$

The probability the next call arrives after 2 hours.

$\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488$

The number of calls recieved each day is recorded for 50 consecutive days.

for 50 days;

$\lambda = 0.3 * 50 * 24 = 360$

The mean = 360

The standard deviation is given as

$S.D = \sigma =\sqrt{360} = 18.974\\$

The probability the sum of these 50 number is less than 356 is

$p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165$

Learn more on poission formula here;

brainly.com/question/7879375

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2 years ago