The heights of horses who compete in the Melbourne Derby are normally distributed with a mean of 66 inches and a standard deviation of 3 inches (a) If a horse is randomly selected from this race, what height would you expect it to be? (b) What percentage of horses who compete in the Melbourne Derby have heights between 60 and 72 inches? (c) In a particular year there are 25 horses running in the Melbourne Derby. How many of these would you expect to have a height of less than 63 inches?

Kindly check explanation

Step-by-step explanation:

Given that:

Distribution = Normal

Mean(m) = 66

Standard deviation (σ) = 3 inches

A.) If horse is randomly selected from the race, Expected height = mean of the distribution = 66

B.) % horses with height between 60 and 72

Using the relation :

X = 60 ; 72

Z = (x - mean) σ

Z = (60 - 66) / 3

Z = - 6/3

Z = - 2

P(Z < - 2) = 0.0228 (using table)

Z = (72 - 66) / 3

Z = 6/3

Z = 2

P(Z < 2) = 0.9772 (using table)

P(score being between 60 and 72):

0.9772 - 0.0228= 0.9544

C) number of samples = 25

Height less than 63 inches :

the answer is 844

step-by-step explanation:

it is 844 because if you add 836.50 + 7.5 you will get 844

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).