Question

Suppose there enists a population where 30% of its members possess a certain charactenstic. Let pi be the proportion of a random sample of 164 members that alse pessess that certain characterutic. Determine the follewing probebilities. Round solutions to four decimal places, if necestany. Find the probability that the sample proportion in reater than 0.14 . P( j^>0.36) Find the probability that the sample proportion is betwene 6.36 aud 0.4. P(0.20< p^<0.4)

Answer 1

To find the probability that the sample proportion is greater than 0.14, calculate the Z-score and use a Z-table to find the probability. The probability is approximately 0.03%.

Step-by-step explanation:

To find the probability that the sample proportion is greater than 0.14, we need to calculate the Z-score and then use a Z-table to find the probability.

The formula to calculate the Z-score is Z = (p^ - p) / sqrt((p * q) / n), where p^ is the sample proportion, p is the population proportion, q is 1 - p, and n is the sample size.

Using the given values, we have p = 0.3, p^ = 0.14, q = 0.7, and n = 164. Plugging in these values, we get Z = (0.14 - 0.3) / sqrt((0.3 * 0.7) / 164) = -3.408.

We can now use the Z-table to find the probability associated with a Z-score of -3.408. From the table, we can see that the probability is approximately 0.0003 or 0.03%.