Question

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.

Answer 1

Answer:

See answer in attachment.

Step-by-step explanation:

Answer 2

Answer:

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.