Question

at one college GPAs have a distribution that is unimodal and symmetric with a mean of 2.7 and s standard deviation of 0.5. Is a GPA of 3.8 more than one standard deivation from the mean?

Answer 1

Answer:

Yes, a GPA of 3.8 is more than one standard deviation from the mean

Step-by-step explanation:

Let X = student's college GPA.

The random variable X follows a Norma distribution (since it is uni-modal and symmetric) with parameter μ = 2.7 and σ = 0.5.

To determine whether a GPA of 3.8 is more than one standard deviation from the mean, compute the percentile ranks of each GPA.

Compute the probability of getting a GPA less than 3.8 as follows:

$P(X$

*Use a z-table for the probability.

The GPA of 3.8 is at the 99th percentile.

Compute the probability of getting a GPA less than (μ + σ) as follows:

$P(X$

*Use a z-table for the probability.

The GPA of (μ + σ =) 3.2 is at the 84th percentile.

Since the percentile rank of GPA 3.8 is more than the percentile rank of GPA 3.2, i.e. one standard deviation from the mean, it can be concluded that a GPA of 3.8 is more than one standard deviation from the mean.