Statistics and Probability Answers

Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. Find the probability (by hand and using MS Excel) that a call takes: 3 minutes or less.

exceed 5 minutes

A sample of 𝑛=20

n

=

20

 observations is drawn from a normal population with 𝜇=950

μ

=

950

 and 𝜎=250

σ

=

250

. Find each of the following:

A. 𝑃(𝑋

¯

>1061)

P

(

X

¯

>

1061

)

Probability = 

B. 𝑃(𝑋

¯

<838)

P

(

X

¯

<

838

)

Probability = 

C. 𝑃(𝑋

¯

>894)

P

(

X

¯

>

894

)

Probability = 

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 60 miles and a standard deviation of 5 miles. Find the probability of the following events:

A. The car travels more than 67 miles per gallon.

Probability =  

B. The car travels less than 53 miles per gallon. 

Probability =  

C. The car travels between 52 and 67 miles per gallon. 

Probability =  

“A histogram is a graphical representation of tabulated frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), with an area equal to the frequency of the observations in the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data.”

a.      Find a frequency distribution of letters of the alphabet in the English language from a given paragraph.

(Hint: A, B, C, ..., Z)

b.     Find relative frequency distribution.

c.      Present percentage frequency distribution in most suitable graph.

d.     Which letter occurs most frequently?

e.      Which letter occurs least?  

A certain restaurant soon to be open. In the process of preparing, they have to buy appliances. A refrigerator,which cost 45,789 has a 15% chance of replacement in the first three years of purchase. The store is offering an extension of the warranty cost of 8,785 oh the refrigerator.

a. What is the expected value of the extended warranty assuming it is replaced after years?

b. will you buy the refrigerator? Why?

c. what is the mean, variance and standard deviation?

Borden et al. (A-24) performed experiments on cadaveric knees to test the effectiveness of several meniscal repair techniques. Specimens were loaded into a servohydraulic device and tension-loaded to failure. The biomechanical testing was performed by using a slow loading rate to simulate the stresses that the medial meniscus might be subjected to during early rehabilitation exercises and activities of daily living. One of the measures is the amount of displacement that occurs. Of the 12 specimens receiving the vertical mattress suture and the FasT-FIX method, the displacement values measured in millimeteres are 16.9, 20.2, 20.1, 15.7, 13.9, 14.9, 18.0, 18.5, 9.2, 18.8, 22.8, 17.5. Construct a 90 percent confidence interval for the variance of the displacement in millimeters for a population of subjects receiving these repair techniques.

find the regression analysis, what is the value of a,b, and what is expected y if x=18

X: 17 12 10 20

Y: 10 10 8 12

Problem Solving. Compute for the hypothesis test values of the given problem. Show the five necessary steps.

A psychiatrist is testing a new anti-anxiety drug, which seems to have the potentially harmful side effect of lowering the heart rate. For a sample of 50 medical students whose pulse was measured after 6 weeks of taking the drug, the mean heart rate was 70 beats per minute (bpm). If the mean heart rate for the population is 72 bpm with a standard deviation of 12, can the psychiatrist conclude that the new drug lowers heart rate significantly? (Set the level of significance to 0.01.) 

SOLUTIONS:

Step 1: State the hypotheses.

Ho: 

Ha:

Step 2: The level of significance and the critical region. 𝛼 = _____, 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 = _____. 

Step 3: Compute for the value of one sample test.

𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑑 𝑡𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 = _______. 

Step 4: Decision rule.

Step 5. Conclusion.