Question

1. The numbers of incorrect answers on a true false competency test for a random sample of 15 students were recorded as follows: 2, 1,3,0, 1, 3, 6, 0,3,3,5, 2, 1, 4, and 2. Find (a) the mean; (b) the median; (c) the mode. 2. The grade-point averages of 20 college seniors selected at random from a graduating class are as follows: 3.2 1.9 2.7 2.4 2.8 2.9 3.8 3.0 2.5 3.3 1.8 2.5 3.7 2.8 2.0 3.2 2.3 2.1 2.5 1.9 Calculate the standard deviation. 3. The average life of a bread-making machine is 7 years, with a standard deviation of 1 year. Assuming that the lives of these machines follow approximately a normal distribution, find (a) the probability that the mean life of a random sample of 9 such machines falls between 6.4 and 7.2 years; (b) the value of x to the right of which 15% of the means computed from random samples of size 9 would fall. 4. A manufacturing firm claims that the batteries used in their electronic games will last an average of 30 hours. To maintain this average, 16 batteries are tested each month. If the computed t-value falls between as and, the firm is satisfied with its claim. What conclusion should the firm draw from a sample that has a mean of 1 = 27.5 hours and a standard deviation of s=5 hours? Assume the distribution of battery lives to be approximately normal. 5. A machine produces metal pieces that are cylindrical in shape. A sample of pieces is taken, and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. Find a 99% confidence interval for the mean diameter of pieces from this machine, assuming an approximately normal distribution. 6. Assume x obeys a normal distribution (4,0°), and X., X.X.is

Answer 1

Answer:-

Given That:-

The numbers of incorrect answers on a true-false competency testfor a random sample of 15 students were recorded as follows: 2, 1,3, 0, 1, 3, 6, 0, 3, 3, 5, 2, 1, 4, and 2. Find:
a.
Mean
b.
Median
c.
Mode.

a. Mean

Given,

From the given data is as follows 2, 1,3, 0, 1, 3, 6, 0, 3, 3, 5, 2, 1, 4, and 2.

Here the sample size n = 15

  = 36/15

= 2.4

b. Median

Arrange the given data in ascening order 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 6.

Here the sample size n is odd.

So the median value is the  

Median  

c. Mode

Any value that occurs with the greatest frequency is a mode of the data set.

From the data we calculate frequencies of each observation

X

Frequency

0

2

1

3

2

3

3

4

4

1

5

1

6

1

The greatest frequency is 4, and that 3 is the only value that occurs with that frequency.

So the mode is 3.

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