Question #345728
  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?




1
Expert's answer
2022-05-30T17:10:55-0400

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


2.

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

z=1.2816z=1.2816

Find the upper 10% of the normal curve is z=1.2816.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=1.4758P(Z<z)=0.93=>z=1.4758

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

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

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

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

5.

μ=80,s=15\mu=80, s=15


P(X<84)=P(Z<848015)P(X<84)=P(Z<\dfrac{84-80}{15})

P(Z<0.2667)0.6051\approx P(Z<0.2667)\approx0.6051

The percentile rank of a score of 84 is 60.5.



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