Answer:

To construct the sampling distribution, we need to list all the possible outcomes of tossing a coin thrice and record the values of 1 or 0. There are 2^3 = 8 possible outcomes:

HHH, HHT, HTH, THH, HTT, THT, TTH, TTT

The recorded values are:

HHH = 1 1 1

HHT = 1 1 0

HTH = 1 0 1

THH = 0 1 1

HTT = 1 0 0

THT = 0 1 0

TTH = 0 0 1

TTT = 0 0 0

a. Sample mean:

To find the sample mean, we add up all the recorded values and divide by the sample size, which is 8.

Recorded values: 1 1 1 1 1 0 0 0

Sample mean = (1 + 1 + 1 + 1 + 1 + 0 + 0 + 0) / 8 = 0.625

The sampling distribution for the sample mean is as follows:

Sample mean Probability

0.000 1/8

0.125 3/8

0.250 3/8

0.375 1/8

b. Sample mode:

The sample mode is the value that appears most frequently in the recorded values. In this case, both 0 and 1 appear three times, so there is no unique sample mode.

The sampling distribution for the sample mode is as follows:

Sample mode Probability

0 0.5

1 0.5

c. Sample range:

The sample range is the difference between the highest and lowest recorded values. The possible ranges are 0, 1, and 2.

The sampling distribution for the sample range is as follows:

Sample range Probability

0 1/4

1 1/2

2 1/4

d. Sample max:

The sample max is the highest recorded value. The possible values are 0 and 1.

The sampling distribution for the sample max is as follows:

Sample max Probability

0 1/2

1 1/2

e. Sample min:

The sample min is the lowest recorded value. The possible values are 0 and 1.

The sampling distribution for the sample min is as follows:

Sample min Probability

0 1/2

1 1/2