Suppose the test scores on a final exam are normally distributed with a mean of 74 and a standard deviation of 3. What is the probability that a randomly selected test has a score higher than 77?

We have been given that the test scores on a final exam are normally distributed with a mean of 74 and a standard deviation of 3. We are asked to find the probability that a randomly selected test has a score higher than 77.

First of all, we will find z-score corresponding to sample score 77.

, where,        

z = z-score,

x = Random sample score,

= Mean,

= Standard deviation.

Now we need to find .

We will use formula to find the probability greater than a z-score of 1.

Using normal distribution table, we will get:

Therefore, the probability that a randomly selected test has a score higher than 77 would be 0.15866.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.