Question

1. Kelly and Veronica are two teachers in a math class who attend class independently of one another. For Friday classes, there is a .70 probability that kelly will come to class, while there is a .40 probability that Veronica will come to class. For a Friday class, what is the probability neither Kelly nor Veronica will be there?

2.  The weights of newborn baby twin girls have an approximately normal distribution with a mean of 8.0 pounds and a standard deviation of 1.5 pounds. A doctor tells the family that one of the baby twin girl has a weight at the 30th percentile. Which of the following is closest to this baby's weight? (show work please)

A, 7.2

B 8.5

C 7.7

D 8.9

Answer 1

1.

Let, K be the event that Kelly will come to class

Let, V be the event that Veronica will come to class

Probability that Kelly will come to class = P(K) = 0.7

Probability that Kelly will not come to class = P(K) = 1 - P(K) = 1 - 0.7 = 0.3

Probability that Veronica will come to class = P(V) = 0.4

Probability that Veronica will not come to class = P(V) = 1 - P(V) = 1 - 0.4 = 0.6

Since, 1. Kelly and Veronica are two teachers in a math class attend classes independently of one another

Probability neither Kelly nor Veronica will be there = Probability that Kelly will not come to class*Probability that Veronica will not come to class = P(K)*P(V) = 0.6*0.3 = 0.18

Probability neither Kelly nor Veronica will be there = 0.18

2. Let X be the weights of newborn baby twin girls have an approximately normal distribution

mean of X , E(X) =  8.0 pounds

Standard deviation = S(X) =1.5 pounds.

30th percentile mean 30% girls weigh lesser than that of her.

Let, 30th percentile be p_30

P[ X < p_30 ] = 30% = 0.3

X ~ N(8,2.25)

P[ X < p_30 ] = 0.3

P[ ( X - E(X) )/S(X) < ( p_30 - E(X) )/S(X) ] = 0.3

P[ ( X - 8 )/1.5 < ( p_30 - 8 )/1.5 ] = 0.3

P[ Z < ( p_30 - 8 )/1.5 ] = 0.3

Also, we know that

P[ Z < -0.52 ] = 0.3

Comparing, ( p_30 - 8 )/1.5 = -0.52

p_30 - 8 = 1.5*(-0.52)

p_30 - 8 = -0.78

p_30 = 8 - 0.78

p_30 = 7.22

Correct answer is a) = 7.2 pounds