Question

Part B. Fully answer all of the following. 5 points each. 1. The following data represent the flight time (in minutes) of a random sample of five flights from Las Vegas, Nevada to Newark, New Jersey. 282 mins., 270 mins., 260 mins., 266 mins., 257 mins Compute the sample variance and the sample standard deviation. 2. Draw a standard normal curve and shade the area that is to be found. Be sure to label all relevant points. Determine the area under the standard normal curve that lies to the left of... a. Z= -2.45 b. Z= 1.35 c. Z= 3.49 3. Explain the Empirical Rule. 4. Harley Davidson Stock. Harley Davidson stock traded for 40 days in 2000 a random sample of the volume was collected with a mean "X-bar"= .77 million shares and a standard deviation "sigma" o= .94. Construct a 95% confidence

Answer 1

First question is being answered here.

1. First we will calculate the Arithmetic mean as per below:

Formula for Arithmetic Mean is:

Arithmetic Mean (AM) = Sum of the data / No. of data

Sum of the returns = 282 + 270 + 260 + 266 + 257 = 1335

No. of data  = 5

Arithmetic Mean = 1335 / 5 = 267

Steps for calculating standard deviation are:

First we will calculate the deviation of data from the mean data value as per below:

1st: 282 - 267 = 15

2nd : 270 - 267 = 3

3rd: 260 - 267 = - 7

4th: 266 - 267 = - 1

5th: 257 - 267 = - 10

In the next step, we will square the deviations computed above, as per below:

1st:  (15)² = 225

2nd : (3)² = 9

3rd: (-7) = 49

4th:  (-1)² = 1

5th: (-10)² = 100

In the next step we will add up the values calculated above:

Sum of squared deviations = 225 + 9 + 49 + 1 + 100 = 384

In the next step we will calculate the sample variance by the following formula:

Sample Variance = Sum of squared deviations / N- 1

where, N is the no. of data, which is 5 here.

Putting the values in the above equation, we get,

Sample variance = 384 / 5-1

Sample variance = 384 / 4 = 96

In the final step, we will square root the sample variance calculated above to find the sample standard deviation:

Sample standard deviation = (96)^1/2 = 9.7979