Question

Using the normal distribution approximation, give an interval in which you would expect x almost certainly to fall if truly p = 0.50. Fill in the blanks:

a) (-1.96, 1.96)
b) (-0.25, 0.25)
c) (-2.58, 2.58)
d) (-0.50, 0.50)

Answer 1

The correct interval in which you would expect x almost certainly to fall if truly p = 0.50 is (-1.96, 1.96).

Step-by-step explanation:

The correct answer is a) (-1.96, 1.96).

According to the normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean. Since the standard deviation is 6, the interval is calculated as (mean - 2 * standard deviation, mean + 2 * standard deviation). Plugging in the values, we get (50 - 2 * 6, 50 + 2 * 6) = (38, 62). Therefore, the correct interval is (-1.96, 1.96).