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Answer :
Final answer:
The probability that the sample mean is between 85 and 92 is approximately 0.5888.
Explanation:
To find the probability that the sample mean is between 85 and 92, we can follow these steps:
1. Convert the values to z-scores using the formula: z = (x - μ) / (σ / √n).
- For the lower bound, 85: z1 = (85 - 90) / (15 / √25) = -1.
- For the upper bound, 92: z2 = (92 - 90) / (15 / √25) = 0.6667.
2. Use the standard normal distribution table to find the probability between these z-scores. The z-score of -1 corresponds to a probability of approximately 0.1587, and the z-score of 0.6667 corresponds to a probability of approximately 0.7475.
3. To find the probability between these z-scores, subtract the probability corresponding to the lower z-score from the probability corresponding to the upper z-score:
- Probability = 0.7475 - 0.1587 = 0.5888.
Therefore, the probability that the sample mean is between 85 and 92 is approximately 0.5888.
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