An environmental group is interested in what percentage of Americans consider climate change an immediate threat to humanity. From a representative list of 20677 American citizens, they randomly sampled 30; all responded to their questions. They will consider the sample proportion of respondents that agree climate change is an immediate threat to humanity. Previously, 35% of Americans considered climate change an immediate threat to humanity; assume this has not changed. 1. Is it appropriate to use normal distribution to describe the sampling distribution of sample proportion?
a. Yes, because 10.5 and 19.5 are greater than 10.
b. Yes, because 30 American citizens were sampled.
c. No, because this problem concerns the sample proportion instead of the population proportion.
d. No, because the sampling distribution is skewed.
2. Calculate the probability the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35%

(1) Yes, because 30 American citizens were sampled.

(2) The probability that the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is 0.50.

Step-by-step explanation:

We are given that from a representative list of 20677 American citizens, they randomly sampled 30; all responded to their questions.

Previously, 35% of Americans considered climate change an immediate threat to humanity; assume this has not changed.

(1) Yes, it is appropriate to use a normal distribution to describe the sampling distribution of sample proportion because 30 American citizens were sampled.

(2) The z-score probability distribution for the sample proportion is given by;

                          Z =  ~ N(0,1)

where, = sample proportion of Americans who agree climate change is an immediate threat to humanity

p = population proportion of Americans who considered climate change is an immediate threat to humanity

n = sample of American citizens = 30

Now, the probability that the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is given by = P( > 35%)

        P( > 35%) = P( > ) = P(Z > 0) = 0.50

The above probability is calculated by looking at the value of x = 0 in the z table which has an area of 0.50.

Hence, the required probability is 0.50.