Answer to Question #345728 in Statistics and Probability for Eli

Question

1. Solve the problems below. Show your solutions completely.

1. Find the 95th percentile of a normal curve.

2. Find the upper 10% of the normal curve.

3. Where does the 50th percentile lie under the normal curve?

4. A teacher mark the performance of the students in terms of their relative standing in class. Find the z values that corresponds to each of the given information.

Mary Anne – 93% Agnes – 50% Edith – 78%

Roland – 81% Kyle – 96%

5. The results of a nationwide aptitude test in Math are normally distributed with m = 80 and s =15. What is the percentile rank of a score of 84?

Answer 1

1. The 95th percentile of a normal curve is $z=1.6449.$

2.

$$P(Z>z)=0.1$$

$$z=1.2816$$

Find the upper 10% of the normal curve is $z=1.2816.$

3. The 50th percentile gives the point where half (50%) of the data is below and half the data is above the number.

We also call the 50th percentile the median.

The mean, median, and mode all have a corresponding z-score of 0 and are the 50th percentile.

4.

$$P(Z<z)=0.93=>z=1.4758$$

$$P(Z<z)=0.5=>z=0$$

$$P(Z<z)=0.78=>z=0.7722$$

$$P(Z<z)=0.81=>z=0.8779$$

$$P(Z<z)=0.96=>z=1.7507$$

5.

$\mu=80, s=15$

$$P(X<84)=P(Z<\dfrac{84-80}{15})$$

$$\approx P(Z<0.2667)\approx0.6051$$

The percentile rank of a score of 84 is 60.5.