Question

In a school girl's heights are normally distributed w/ a mean of 5'4" and a standard deviation of 2".
a)What is the probability of a randomly chosen girl being taller than 5'5"?
b) If the principal chooses 5 girls at random, what is the probability that at least 4 of them are tallker than 5'5"?

Answer 1

i got 52% for A)

Answer 2

damn this is a higher level of probability, and i totally forgot how to do this kind of questions. Gimme some time i go refresh my memory. Btw are you singaporean?

Answer 3

lol no i'm korean american :)

Answer 4

Okay, first you must understand that the heights are normally distributed. so calculate the z-value to get the distribution of those values in a normal distribution curve. (in simpler terms, to calculate z-value means to adjust the values given to fit in the standard normal distribution curve)

So the z-value for being SHORTER than or EQUAL to 5'5" = (5'5" - 55'4") / 2" = 0.5
The associated probability for z value of 0.5 is 0.70 ( http://www.math.unb.ca/~knight/utility/NormTble.htm)

Since you want the probability of the girl TALLER than 5'5", 1- 0.7 = 0.3


b) If the principal chooses 5 girls at random, what is the probability that at least 4 of them are tallker than 5'5"?
P ( at least 4 girls taller than 5"5") = P (4 girls taller than 5'5") + P( 5 girls taller than 5'5") = 0.3*0.3*0.3*0.3*0.7 + 0.3*0.3*0.3*0.3*0.3= 0.0081

Answer 5

z score = ( 5.5 - 5.4 ) / 2 = .05
=> P ( .05 ) = .4801

Answer 6

shouldn't you convert 5'5" and 5'4" into inches since the standard deviation is in inches?

Answer 7

@tiaph why is it P (4 girls taller than 5'5") + P( 5 girls taller than 5'5") ?

Answer 8

I didnt convert because, 5ft5 inches - 5ft4inches = 1 inch
and 1 inch /2 inch = 0.5

Answer 9

Cause the question ask for at least 4 girls taller than 5'5". meaning 2 situations which you have to take into account.

Situation 1: 4 girls taller than 5'5" and 1 girl shorter or equal to 5'5"
Situation 2: all 5 girls taller than 5'5"

Answer 10

ohhhhhh i remember now
thanks:D!

Answer 11

and if the question is asking if "at most" 4 girls then it would be P(1 girl taller) +P(2girls taller)....+P(4girls taller) right?

Answer 12

yes you got it ;D

Answer 13

w8 shouldn't it be 0.7x0.7x0.7x0.3 +0.7^5 because it's asking for the probability that 4 are taller not shorter?

Answer 14

0.7 is the probability for the girls SHORTER or EQUAL to 5'5". If you want taller 0.3 is the answer you are looking for. Don't get confused.

Answer 15

but if you look at it