A community college has a math placement exam that has a mean of 65 and a standard deviation of 8.2. If a student takes the exam and scores in the lower 2.5%, they are eligible for a free intensive course to help them succeed in their math class. Assume that the exam has a normal distribution. What is the score that cuts off the bottom 2.5%

The score that cuts off the bottom 2.5% is 48.93.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

What is the score that cuts off the bottom 2.5%

This is X when Z has a pvalue of 0.025, so X when Z = -1.96.

The score that cuts off the bottom 2.5% is 48.93.

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !