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Each member of a random sample of 20 business economists was asked to predict the rate of inflation for the coming year. Assume that the predictions for the whole population of business economists follow a normal distribution with a standard deviation of 2%.

What is the value for which the probability is 0.025 that the sample standard deviation is smaller? Round your answer to the nearest second decimal place.

A) 0.98
B) 1.21
C) 1.37
D) 1.42
E) 1.88
F) 2.02
G) 2.43
H) 2.63
I) 2.68
J) 2.76
K) 3.24
L) 3.98
M) 4.76
N) 6.92
O) 7.19
P) None of the above.

Answer :

Final answer:

The value of the sample standard deviation that has a probability of 0.025 is approximately 0.88 when rounded to the nearest second decimal place.

Explanation:

To find the value of the sample standard deviation that has a probability of 0.025, we can look up the corresponding z-score. Using the normal distribution, we can find that the z-score for a probability of 0.025 is approximately -1.96. We can then use the formula for the sample standard deviation to find the value:

Sample standard deviation = (z-score * population standard deviation) / √(sample size)

Sample standard deviation = (-1.96 * 2%) / √(20)

Calculating this value gives us approximately -0.8736, which rounds to 0.88 when rounded to the nearest second decimal place.

Learn more about sample standard deviation here:

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