Suppose that blood chloride concentration(mmol/l) has a normal distribution with mean 110 and standard deviation 4. a. find the probability that chloride concentration equals 111= is less than 111 = is at most 111 = . round to 4 decimal places. b. what is the probability that chloride concentration differs from the mean by more than 2.5 standard deviations? round to 4 decimal places. does this probability depend on the values of μ and σ?

a) P(X = 111) = 0; P(X < 111) = 0.5987; P(X ≤ 111) = 0.5987; b) 0.0124; No

Step-by-step explanation:

For part a, we use z scores.  The formula for the z score of an individual value is

Our mean, μ, is 110 and our standard deviation, σ, is 4.

The probability that x is equal to a given value is 0, regardless of the value, the mean or the standard deviation.  This is because the probability in a normal distribution is the area under the curve; this means there must be a range of numbers.

To find P(X < 111),

z = (111-110)/4 = 1/4 = 0.25

Using a z table, we see that the area under the curve to the right of this is 0.5987.

For P(X ≤ 111), we use the same probability as P(X < 111).  There is no distinction between "less than" and "less than or equal to."

For part b,

2.5 standard deviations above the mean is z = 2.5.  2.5 standard deviations below the mean is z = -2.5.

Using the z table, the area under the curve to the right of z = 2.5 is 0.9938.  The area under the curve to the right of z = -2.5 is 0.0062.  This makes the area between them

0.9938-0.0062 = 0.9876.  This means anything farther from the mean than this is

1-0.9876 = 0.0124.  This does not have anything to do with the value of the mean or the standard deviation; this is because we already have the z score.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!