Question

The GPA's at RHS are Normally distributed with a mean of 2.8 and a standard deviation of 0.7. Let G = a random student's GPA.

Answer 1

The value of  P(G<2.5) is 14.23%.

What is observation?

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. Using scientific tools to perceive and record data is another way that observation may be used in science.

The $z$-score for this observation of 2.30 is:

Z= (2.3-2.8)/0.7=-1.71

The table shows a value of 0.8577 , and because this z-score is negative, this is the proportion greater than a GPA of 2.30. So the proportion less than 2.30 is 1-0.8577 =0.1423 . Expressing it mathematically we have:

$\begin{aligned}P(X \leq 2.7) & =P(Z \leq-1.07) \\& =1-P(Z \geq-1.07) \\& =1-P(Z \leq 1.07) \\& =1-0.8577 \\& =0.1423=14.23 \%\end{aligned}$

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