Question

1) A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 55 miles and a standard deviation of 6 miles. Find the probability of the following events:

A. The car travels more than 59 miles per gallon.

Probability =

B. The car travels less than 51 miles per gallon.

Probability =

C. The car travels between 50 and 63 miles per gallon.

Probability =

2) A sample of ?=24n=24 observations is drawn from a normal population with ?=1000μ=1000 and ?=240σ=240. Find each of the following:

A. ?(?¯>1097)

Probability =

B. ?(?¯<906)

Probability =

C. ?(?¯>990)

Probability =

3) A boxplot for a set of 96 scores is given below.

How many scores are represented in the blue section of the boxplot?
Answer: ?

4)A boxplot for a set of data is given below. Find the five-number summary

Find the minimum:

Find ?1

Find the median

Find ?3:

Find the maximum

Answer 1

1)

a)

P(Y > 59) = P(Y - mean > 59 - mean)
                  = P( (Y - mean)/SD > (59 - mean)/SD
                  = P(Z > (59 - mean)/SD)
                  = P(Z > (59 - 55)/6)
                  = P(Z > 0.667)
                  = 1 - P(Z <= 0.667)
                  = 0.252

b)

P(Y < 51) = P(Y - mean < 51 - mean)
                  = P( (Y - mean)/SD < (51 - mean)/SD
                  = P(Z < (51 - mean)/SD)
                  = P(Z < (51 - 55)/6)
                  = P(Z < -0.667)
                  = 0.252

c)

P(50 < Y < 63) = P(50 - mean < Y - mean < 63 - mean)
                  = P((50 - mean)/SD < (Y - mean)/SD < (63 - mean)/SD)
                  = P((50 - mean)/SD < Z < (63 - mean)/SD)
                  = P((50 - 55)/6< Z < (63 - 55)/6)
                  = P(-0.833 < Z < 1.333)
                  = P(Z < 1.333) - P(Z <-0.833)
                  = 0.707

we are allowed to solve one question only.please post remaining questions separately.