The college boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean of 513 and a standard deviation of 130. these scores are close to being normally distributed. what percentage of the scores can be expected to satisfy each of the following conditions? a. greater than 600 b. greater than 700 c. less than 450 d. between 450 and 600 bus. 4.71 monthly sales figures for a particular

a) 25.14% percentage of the scores expected to be greater than 600.

b) 7.49% percentage of the scores expected to be greater than 700.

c) 31.56% of the scores are expected to be less than 450.

d) 43.3% of the scores are expected to be between 450 and 600.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

For this problem, we have that:

The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean of 513 and a standard deviation of 130, so .

What percentage of the scores can be expected to satisfy each of the following conditions?

a) Greater than 600

This is 1 subtracted by the pvalue of Z when

has a pvalue of 0.7486.

So there is a 1 - 0.7486 = 0.2514 = 25.14% percentage of the scores expected to be greater than 600.

b) Greater than 700

This is 1 subtracted by the pvalue of Z when

has a pvalue of 0.9251.

So there is a 1 - 0.9251 = 0.0749 = 7.49% percentage of the scores expected to be greater than 700.

c. Less than 450

This is the pvalue of Z when

has a pvalue 0.31561.

So, 31.56% of the scores are expected to be less than 450.

d. Between 450 and 600

This is the subtraction of the pvalue of by the pvalue of

So

43.3% of the scores are expected to be between 450 and 600.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

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 ☺