Answer to Question #309889 in Statistics and Probability for badshah

Question

Colombo City typically has rained on about 16% of days in November.

a. What is the probability that it will rain on about 16% of days in November?

b. What is the mean number of days with rain in November?

c. What is the variance and standard deviation of the number of days with rain

in November?

Answer 1

Probability of having the rain (p) = 0.16

Probability of not having the rain (q)= 1-0.16=0.84

Number of days in the month of November (n)=30

a) The probability that it will rain on about 16%of days in November is 0.16

b)The mean number of days with rain in November

mean = $n*p$

$=30*0.16=4.8$

c) The variance and the standard deviation of the number of days with rain in November.

Variance $=n*p*q$

$=30*0.16*0.84$

$=4.032$

Standard deviation $= ​ \sqrt{Variance}$

$= ​ \sqrt{4.032}$

$=2.008$7984064

The variance is 4.032 and the standard deviation is approximately 2.008.