The following are questions from a self-quiz. according to some study, the height for northern european adult males is normally distributed with an average of 181 centimeter and a standard deviation of 7.3 centimeter. suppose such an adult male is randomly chosen. let x be height of that person. the next 2 questions correspond to this information. the answer may be rounded up to 3 decimal places of the actual value. a) the probability that the person is between 160 and 170 centimeters isb) the probability that the person is higher than 190 centimeter is

a) 0.064

b) 0.109

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 181 centimeter

Standard Deviation, σ = 7.3 centimeter

We are given that the distribution of height for Northern European adult males is a bell shaped distribution that is a normal distribution.

Formula:

a) P(person is between 160 and 170 centimeters)

b) P(person is higher than 190 centimeter)

P(x > 190)

Calculation the value from standard normal z table, we have,  

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be