Answer to Question #139725 in Statistics and Probability for Sohyun Ravena

Question

II. Given sigma μ=45 and σ, = 6, determine and plot the location of the z scores of the following raw scores: 56, 70,82
III. The scores of SLU College Admission Test are normally distributed,with = 80 and = 6. Find the following:
1. What is the percentile rank of 84?
2. What percentageof scores fall between 64 and 90?

Answer 1

$$Z=\frac{x-\mu}{\sigma}$$

Part I)

$$\mu = 45, \ \sigma=6$$

When X = 56,

$$Z=\frac{56-45}{6}= 1.8333$$

When X = 70

$$Z=\frac{70-45}{6}=4.1667$$

When X = 82

$$Z=\frac{83-45}{6}=6.1667$$

Part II)

$$\mu =80,\ \sigma =6$$

1.) At 84,

$$Z=\frac{84-80}{6}=0.6667$$

At Z= 0.6667, probability is 0.74752.

The percentile score 74.752

2. Between 64 and 90

$$\frac{64-80}{6} < Z < \frac{90-80}{6}$$

$$-2.6667<Z<1.6667$$

The corresponding probability is

$P(Z<1.6667)-P(Z>-2.6667)$

$$0.95221-0.00383=0.94838$$

the probability is 0.9484