Question

1

1. Jonathan weighs 121 pounds. What is his percentile rank given that the average weight of the normally distributed population (μ) is 99 pounds with a standard deviation (σ) of 10 pounds?

2. Sarah has an IQ of 121 and Tom has an IQ of 89. What percentage of the normally distributed population, which has an average IQ scores (μ) of 100 with a standard deviation (σ) of 15 has a score between their two scores?

Answer 1

Solution(1)
Given in the question
weight of the normally distributed population with
Mean () = 99
Standard deviation() = 10
If Jonathan weighs 121 pounds than percentile can be calculated as P(X<121) =?
Here we will use the standard normal distribution, First, we will calculate Z-score which can be calculated as

Z=(X-)/ = (121-99)/10 = 2.2
From Z table we found a p-value
P(X<121) = 0.9861
So Jonathan's percentile is 98.61.
Solution(2)
Mean () = 100
Standard deviation() = 15
Sarah has an IQ of 121 and Tom has an IQ of 89 we need to calculate percentage of normal distribution curve between 89 and 121 i.e. P(89<X<121) = P(X<121) - P(X<89)

Here we will use the standard normal distribution, First, we will calculate Z-score which can be calculated as

Z=(X-)/ = (89-100)/15 = -0.73
Z= (121-100)/15 = 1.4
From Z table we found a p-value
P(89<X<121) = P(X<121) - P(X<89) = 0.9192 - 0.2327 = 0.6865
So there is 68.65% of the normal curve is between 89 and 121