SMAT-1580 Written Assignment 5 Sections 5.1-5.2 1. (2 pts) Find the mean and sta

Question

SMAT-1580 Written Assignment 5 Sections 5.1-5.2 1. (2 pts) Find the mean and standard deviation for the number of girls in 8 births. 2. (2 pts) Find probability of getting exactly 5 girls in 8 births 3. (2 pts) Find probability of getting 1 or fewer girls in 8 births. Is 1 a significantly low number of girls in 8 births. (4 pts) Approximately 3% ofthe eggs in a store are cracked. If you buy two dozen eggs, what is the probability that 4. a) b) c) none of your eggs are cracked at least one of your eggs is cracked exactly two of your eges are cracked

Explanation / Answer

Ans:

1)n=8

Probability of being a girl=p=0.5

mean=np=8*0.5=4

standard deviation=sqrt(8*0.5(1-0.5)=1.414

2)Let x be the number of girls in 8 births.

P(x=5)=8C5*0.5^5*(1-0.5)^3=0.21875

3)

P(x<=1)=P(x=0)+P(x=1)

=(1-0.5)^8+8C1*0.5^1*(1-0.5)^7

=0.0039+0.0313

=0.0352

4)n=24,p=0.03

a)P(none)=(1-0.03)^24=0.4814

b)P(atleast one)=1-P(none)=1-0.4814=0.5186

c)P(exactly 2)=24C2*0.03^2*(1-0.03)^22=0.1271

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