Question

10. A normal population has mean u = 7 and standard deviation o = 5. Find the proportion of the population that is between –2 and 10. 11. A population has mean pu=53 and standard deviation o = 34. Find the value that has 35% of the population above it.

show work write on paper please

Answer 1

Solution :

Given that ,

10) mean = $\mu$ = 7

standard deviation = $\sigma$ = 5

P( - 2< x < 10) = P[(- 2 - 7) / 5) < (x - $\mu$ ) /$\sigma$  < (10 - 7) / 5) ]

= P( - 1.8 < z < 0.6 )

= P(z < 0.6) - P(z < - 1.8)

Using z table,

= 0.7257 - 0.0359

= 0.6898

Given that ,

11) mean = $\mu$ = 53

standard deviation = $\sigma$ = 34

Using standard normal table,

P(Z > z) = 35%

= 1 - P(Z < z) = 0.35  

= P(Z < z) = 1 - 0.35

= P(Z < z ) = 0.65

= P(Z < 0.39) = 0.65  

z = 0.39

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 0.39 * 34 + 53

x = 66.26