Question

A class of 40 students, 18 are males and 22 are females. For the final examination, 3 males and 5 females achieved a letter grade of A. What is the probability that a randomly selected student from the class achieved letter A grade or is a female student?

Select one:

a. 27/40

b. 25/40

c. 13/30

d. 30/40

e. 22/40

Suppose it is known that 11% of Canadian are left handed. In a random sample of 500 Canadian, what is the approximate probability that at least 70 of them to be left handed?

Select one:

a. 0.0110

b. 0.0162

c. 0.0287

d. 0.0035

e. 0.0239

The mean yield of alfalfa from a particular plot of land has been stable at 25 kilograms. The agronomist believes that a new fertilizer will result in an increased yield of alfalfa. The agronomist tested the new fertilizer on 16 equal sized plots of land and determines the yield to be 25.4 kilograms. What is the appropriate hypothesis for this test?

Select one:

a. H₀: x̄ = 25 vs. Ha: x̄ < 25

b. H₀: x̄ = 25 vs. Ha: x̄ ≠ 25

c. H₀: µ = 25 vs. Ha: µ ≠ 25

d. H₀: µ = 25 vs. Ha: µ < 25

e. H₀: µ = 25 vs. Ha: µ > 25

A physical-fitness association in Calgary Alberta is including the mile run in its secondary-school fitness test for girls. The time for this event is approximately normally distributed with a mean of 400 seconds and a standard deviation of 40 seconds. If the association wants to select the fastest 5% as “exceptional”, what is the maximum time (in seconds) a runner will need in order to qualify as “exceptional”?

Select one:

a. 520

b. 400

c. 466

d. 334.2

A company packages drought beer in cans. The volume of the cans follow a normal distribution with a standard deviation of 4 ml. If 5% of the cans contain more than 358 ml of beer, what is the mean volume of the canned beers?

Select one:

a. 344.7

b. 360.2  

c. 351.4  

d. 372.0

e. 361.2  

Answer 1

i)

Given

Total number of students =40

Number of males = 18

Number of females= 22

Total number of students that achieved a letter grade A = 3+5 =8

The probability that a randomly selected student from the class achieved letter A grade = 8/40

i.e. P( grade A ) =8/40

The probability that a randomly selected student from the class is a female = 22/40

i.e. P( female) = 22/40

Number of female student that achieved a letter grade A = 5

Probability that a randomly selected student from the class is a female and achieved letter grade A = 5/40

i.e. P( female and grade A) =5/40

Now

The probability that a randomly selected student from the class achieved letter A grade or is a female student = P( grade A) + P(female) – P( female and grade A)

                        = 8/40 + 22/40 – 5/40

                        = 25/40

Therefore, the correct option is b) 25/40

ii)

Probability of Canadian that are left handed = 0.11

i.e. p = 0.11

Number of observation (n) = 500

The normal distribution can be used as an approximation to the binomial distribution for large sample size.

And

X is approximately N(np, npq) where q = 1-p

Mean = = np = 500*0.11 =55

Standard deviation= =

Now

The correct option is b) 0.0162

iii)

The correct option is e. H0: µ = 25 vs. Ha: µ > 25

iv)

Using Z-score calculator or Z table we get

z = -1.645

The raw score is calculated using the formula

So,

Therefore, the correct option is d. 334.2