A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Let X=, the height of a randomly selected student from this set.

The value of P(X < 115) of the students height normally distributed is;

P(Z < -1.75) = 0.04

Given that :

Population Mean; μ = 150

Population Standard deviation; σ = 20

We want to find P(X < 115) which was missing in the question

Let us find the z-score first

Formula for z-score is:

z = (x' - μ)/σ

Plugging in the relevant values gives;

z = (115 - 150)/20

z = -35/20

z = -1.75

From online p-value from z-score calculator, the p-value is;

P(Z < -1.75) = 0.04

Read more about p-value from z-score at; link

The proportion of students whose height are lower than Darnell's height is 71.57%

Step-by-step explanation:

The complete question is:

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Darnel is a middle school student with a height of 161.4cm.

What proportion of proportion of students height are lower than Darnell's height.

We first calculate the z-score corresponding to Darnell's height using:

We substitute x=161.4 , , and to get:

From the normal distribution table, we read 0.5 under 7.

The corresponding area is 0.7157

Therefore the proportion of students whose height are lower than Darnell's height is 71.57%

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is