Scores on a recent national statistics exam were normally distributed with a mean of 82.2 and a standard deviation of 5.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award

The lowest score eligible for an award is 92.

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:

If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award

The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then

The lowest score eligible for an award is 92.

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.