Question

CAN YOU PLEASE ANSWER THESE 3 QUESTIONS !

1. What z value is associated with the least 29%?

2. What z value is associated with the greatest 23%?

3. A normal distribution has a mean of 57.2 and a standard deviation of 13.3. Find the value where the lowest 5% of data ends.

Answer 1

Solution :

Given that,  

Using standard normal table ,

1.

P(Z < z) = 29%

P(Z < -0.55) = 0.29

z = -0.55

z-value = -0.55

2.

P(Z > z) = 23%

1 - P(Z < z) = 0.23

P(Z < z) = 1 - 0.23

P(Z < 0.74) = 0.77

z = 0.74

z-value = 0.74

3.

mean = = 57.2

standard deviation = = 13.3

Using standard normal table ,

P(Z < z) = 5%

P(Z < -1.65) = 0.05

z = -1.65

Using z-score formula,

x = z * +

x = -1.65 * 13.3 + 57.2 = 35.255

value = 35.255