Question

In: Statistics and Probability

Assume that​ women's heights are normally distributed with a mean given by ​, 62.6 and a...

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.

Solutions

Expert Solution

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


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