In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.1 inches and a standard deviation of 4.0 inches. A study participant is randomly selected Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 68 inches. The probability that the study participant selected at random is less than 68 inches tall is (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 68 and 70 inches. The probability that the study participant selected at random is between 68 and 70 inches tall is (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 70 inches. The probability that the study participant selected at random is more than 70 inches tall is (Round to four decimal places as needed) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05. B. The event in part (a) is unusual because its probability is less than 0.05. C. There are no unusual events because all the probabilities are greater than 0.05 D. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.

See answer in attachment.

Step-by-step explanation:

a. 0.49

b. 0.1926

c. 0.3174

d. C. There are no unusual events because all the probabilities are greater than 0.05

Step-by-step explanation:

μ=68.1 and σ=4

a. P(X<68)

The z-score associated with X=68

Z=(X-μ)/σ

Z=(68-68.1)/4

Z=-0.1/4

Z=-0.025

Z=-0.025

P(X<68)=P(Z<-0.025)

P(X<68)=P(-∞<Z<0)-P(0<Z<-0.025)

P(X<68)=0.5-0.01

P(X<68)=0.49

b. P(68<X<70)

Z=(X-μ)/σ

Z-score associated with X=70

Z=(70-68.1)/4

Z=1.9/4

Z=0.475

P(68<X<70)=P(-0.025<Z<0.475)=P(0<Z<-0.025)+P(P(0<Z<0.475)

P(68<X<70)=0.01+0.1826

P(68<X<70)=0.1926

c. P(X>70)

P(X>70)=P(Z>0.475)

P(X>70)=P(0<Z<∞)-P(0<Z<0.475)

P(X>70)=0.5-0.1826

P(X>70)=0.3174

d.

The events are unusual if the probability of an event is less than 5%. As all the events have probabilities greater than 5%, so, no event is unusual.

15

step-by-step explanation:

we are given the following expression and we are to solve it and find the product:

-13 × (-5)

solving the given expression in the standard order of solving a mathematical expression, beginning with the opening of brackets and then multiplying the terms and changing their signs.

-3 × -5 = 15 (answer is positive because when negative is multiplied with negative, it gives a positive answer)

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it