83% of people worldwide fear that a recession is coming within the next 9 months. In a random sample of 12 people, what is the probability that 1) At most 4 people fear that a recession is coming within the next 6 months 2) More than 7 fear that a recession is coming within the next 6 months 3) At least 5 fear that a recession is coming within the next 6 months 4) For x= 0 to 12, determine the probabilities of the event and find the variance and standard deviation of worldwide fear that a recession is coming within the next 6 months.

Please do it in a google spreadsheet and share the link

Here are the answer but I need help to get it into a google spreadsheet

Given Data :

Sample size = n = 12

Probability = p = 83% = 0.83

a) To Find : P(x 4)

By using binomial distribution formula,

P(X = x) = nCx * p^x * (1-p)^(n-x)

Calculations :

P(x 4)= P(x = 0) +P(x = 1)+P(x = 2) +P(x = 3)+P(x = 4)

= [12C0 * (0.83)^0* (1-0.83)^(12-0) + 12C1 * (0.83)^1* (1-0.83)^(12-1)+...+12C4 * (0.83)^4* (1-0.83)^(12-4)]

= 0.0002

P(x 4) = 0.0002

Answer : The Probability that at most 4 out of the 12 is 0.9916

b)To Find : P(x >7)

By using binomial distribution formula,

P(X = x) = nCx * p^x * (1-p)^(n-x)

Calculations :

P(x > 7)= P(x = 8) +P(x = 9)+P(x = 10) +P(x = 11)+P(x = 12)

= [12C8 * (0.83)^8* (1-0.83)^(12-8) + 12C9 * (0.83)^9* (1-0.83)^(12-9)+...+12C12 * (0.83)^12* (1-0.83)^(12-12)]

P(x > 7) = 0.9667

Answer : the probability that more than 7 is 0.9667

c)To Find : P(x 5)

By using binomial distribution formula,

P(X = x) = nCx * p^x * (1-p)^(n-x)

Calculations :

P(x 5)=1-[ P(x = 0) +P(x = 1)+P(x = 2) +P(x = 3)+P(x = 4)]

=1- [12C0 * (0.83)^0* (1-0.83)^(12-0) + 12C1 * (0.83)^1* (1-0.83)^(12-1)+...+12C4 * (0.83)^4* (1-0.83)^(12-4)]

= 1-0.0002

P(x 10) = 0.9998

Answer : the probability that at least 5 out of 12 is 0.8976

Expected value

f) To find expected value

Mean = u = n*p

= 12* 0.83

= 9.96

Mean = u = 9.96

To find standard deviations

standard deviations = n*p*(1-p)

= 12*0.83*(1-0.83)

standard deviations = 1.30

Answer :

1)The Probability that at most 4 out of the 12 is 0.9916

2) the probability that more than 7 is 0.9667

3)the probability that at least 5 out of 12 is 0.8976

4)Mean = u = 9.96

standard deviations = 1.30