Answer to Question #100781 in Statistics and Probability for angana

Question

Colombo City typically has rain on about 16% of days in November.
(a) What is the probability that it will rain on exactly 5 days in November? 15 days?
(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)=16%=0.16

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

No of days in the month of November =30 days

(a) i) The probability that it will rain on exactly 5 days in November

=_nC_rp^rq^n-r=₃₀C₅(0.16)⁵(0.84)^30-5=

=142,506 x 0.0001048576 x 0.0127932873

=0.182

ii) The probability that it will rain on exactly 15 days in November=

₃₀C₁₅(0.16)¹⁵(0.84)^30-15=

=155,117,520 x 8.43313454 x 10^-14

=1.30812692 x 10^-5

b) mean number =np=30x0.16=4.8

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

variance= npq= 30 x 0.16 x0.84=4.032

standard deviation = $\sqrt{variance}=\sqrt{4.032}=2.00798406.$