In: Statistics and Probability
Assume that women's heights are normally distributed with a mean given by , 62.6 and a standard deviation given by 2.8 . (a) If 1 woman is randomly selected, find the probability that her height is less than 63 in. (b) If 49 women are randomly selected, find the probability that they have a mean height less than 63 in.
Solution :
Given that,
mean = = 62.6
standard deviation = =2.8
1 ) P( x < 63 )
P ( x - / ) < ( 63 - 62.6 / 2.8)
P ( z < 0.4 / 2.8 )
P ( z < 0.14)
= 0.5557
Probability = 0.5557
2 )n =49
= 62.6
= / n = 2.8 49 = 0.4
p ( < 63)
P ( - /) < ( 63 - 62.6 /1.1666)
P( z < 0.4 / 0.4 )
P ( z < 1 )
Using z table
= 0.8413
Probability = 0.8413