A humanities professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 64d% C: Scores below the top 366% and above the bottom 23#% D: Scores below the top 77w% and above the bottom 7%7% F: Bottom 7%7% of scores Scores on the test are normally distributed with a mean of 77.877.8 and a standard deviation of 8.58.5. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

The minimum score required for an A grade is 88.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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 problem, we have that:

Find the minimum score required for an A grade.

Top 12%, which is at least the 100-12 = 88th percentile, which is the value of X when Z has a pvalue of 0.88. So it is X when Z = 1.175.

Rounding to the nearest whole number

The minimum score required for an A grade is 88.

the minimum score required for an A grade is 88.

Step-by-step explanation:

Since the scores on the test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = scores on the test.

µ = mean score

σ = standard deviation

From the information given,

µ = 77.8

σ = 8.5

The probability value for the top 12% of the scores would be (1 - 12/100) = (1 - 0.13) = 0.88

Looking at the normal distribution table, the z score corresponding to the probability value is 1.18

Therefore,

1.18 = (x - 77.8)/8.5

Cross multiplying by 8.5, it becomes

1.18 × 8.5 = x - 77.8

10.03 = x - 77.8

x = 10.03 + 77.8

x = 88 to the nearest whole number

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages