Question

5 0063 Central Limit Theorem pages 278-285. If the mean height of women in the U.S.(ages 20-29) is 64 and the standard deviation is 2.75..... What is the probability that a randomly selected woman will have a height of more than 65.61 inches. Assume a normal distribution Show the standard normal graph with Z-scores. Graph is 2 of the 6 points b. What is the probability that 16 randomly selected women will have a mean height of more than 64.2 show standard normal graph with Z-scores. Assume a normal distribution Graph is 2 of the 6 points)

Answer 1

Solution :

Given that ,

mean = $\mu$ = 64

standard deviation = $\sigma$ = 2.75

P(x > 65.61) = 1 - P(x < 65.61)

= 1 - P[(x - $\mu$ ) / $\sigma$ < (65.61-64) / 2.75]

= 1 - P(z < 0.59)

Using z table,

= 1 -0.7224

=0.2776

-3 -2 -1 ó i ż

B.

n = 16

$\mu$_{$\bar x$} = 64

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 2.72/ $\sqrt$ 16= 0.68

P($\bar x$ >64.2 ) = 1 - P($\bar x$ < 64.2)

= 1 - P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (64.2-64) / 0.68]

= 1 - P(z < 0.29)

Using z table,    

= 1 - 0.6141

=0.3859