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.
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
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