A psychology professor assigns letter grades on a test according to the following scheme. A: Top 7% of scores B: Scores below the top 7% and above the bottom 64% C: Scores below the top 36% and above the bottom 25% D: Scores below the top 75% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 78.4 and a standard deviation of 7.6. 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 89.8.

Step-by-step explanation:

We are given that a psychology professor assigns letter grades on a test according to the following scheme. A : Top 7% of scores. B : Scores below the top 7% and above the bottom 64%. C : Scores below the top 36% and above the bottom 25%. D : Scores below the top 75% and above the bottom 6%. F : Bottom 6% of scores.

Scores on the test are normally distributed with a mean of 78.4 and a standard deviation of 7.6.

Let X = Scores on the test

SO, X ~ Normal()

The z-score probability distribution for normal distribution is given by;

                              Z = ~ N(0,1)

where, = mean time = 78.4

            = standard deviation = 7.6

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, the minimum score required for an A grade so that it represents Top 7% of scores is given by;

      P(X x) = 0.07   {where x is the required minimum score

      P( ) = 0.07

       P(Z ) = 0.07

So, the critical value of x in the z table which represents the top 7% of the area is given as 1.4996, that is;

                          = 78.4 + 11.39696 = 89.8 or 90

Hence, the minimum score required for an A grade is 89.8.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺