Question

for all of the normal distribution percentages (probabilities), you need to use the methods shown in class, which requires using a standard normal probability table. if you use technology to do these calculations for you, there might be rounding issues which will mark your answers as incorrect. if you need a copy of the table, you can find it on this website table a - standard normal probabilities
the gpas at a large high school have an approximately normal distribution with a mean of 3.08 and standard deviation of 0.25. what is q3?
q3 =
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Explanation:

Step1: Find the z - score for Q3

The third quartile \(Q3\) corresponds to the \(75^{th}\) percentile. Looking up the \(z\) - score in the standard normal table for a cumulative probability of \(0.75\). The \(z\) - score \(z\approx0.67\)

Step2: Use the formula for the value in a normal distribution

The formula for a value \(x\) in a normal distribution is \(x=\mu + z\sigma\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation. Given \(\mu = 3.08\) and \(\sigma=0.25\)

Substitute the values into the formula: \(x = 3.08+0.67\times0.25\)

First, calculate \(0.67\times0.25 = 0.1675\)

Then, \(x=3.08 + 0.1675=3.2475\)

Answer:

\(3.25\)