Penny\'s birthday is March 3. She is very happy when it snows on her birthday. H

Question

Penny's birthday is March 3. She is very happy when it snows on her birthday. Historical records indicate that the probability of snow on March 3 is 0.29. We will assume that weather on March 3 is independent from year to year and that .29 is the probability of snow on any given March 3. Consider the time period from the year 2019 - 2030. (There are 12 years.) Let X be the number of times it snows on March 3 from 2019-2030.

a. Calculate the expected value of X.  
b. Calculate the variance of X.  
c. Calculate the standard deviation of X.  
d. Calculate the expected value of 5X + 2.  
e. Calculate the variance of 5X + 2.  
f. Calculate the expected value of X2

g. Calculate the probability that X = 3.  
h. Calculate the probability that X is at least 5.  
i Calculate the probability that it does not snow on March 3 at all from 2019-2030.  
j What is the probability that X is within 1 standard deviation of its expected value?  
Add any comments below.

Explanation / Answer

N=12,p=0.29,q=0.71

a) E(x)=np=12*0.29=3.48

b) Var(x)=npq=12*0.29*0.71=2.4708

c) Standard deviation of X= sqrt( 2.4708)=1.572

d) E( 5X+2)= 5*3.48+2=19.5

Please repost the rest of the parts individually

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