Question

#7-8: Given:

Mean= 550 & s=100.

7. What score (x) represents the 77th percentile?

8. Between what two values (x) would the middle 50% of the scores fall?

Answer 1

Solution:-

Given that,

mean = = 550

standard deviation = = 100.

Using standard normal table,

7 ) P(Z < z) = 77%

= P(Z < z) = 0.77

= P(Z < 0.739 ) = 0.77

z = 0.74

Using z-score formula,

x = z * +

x = 0.74* 100.+550

x = 624

8 )The 77th percentile Iis 624P(-z < Z < z) = 50%
P(Z < z) - P(Z < z) = 0.50
2P(Z < z) - 1 = 0.50
2P(Z < z ) = 1 + 0.50
2P(Z < z) = 1.50
P(Z < z) = 1.50 / 2
P(Z < z) = 0.75
z = 0.67 and z = - 0.67

Using z-score formula,

x = z * +

x = 0.67* 100.+550

x = 617

Using z-score formula,

x = z * +

x = -0.67* 100.+550

x = 483