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Answer :
Final answer:
a. The z-score is -0.33. b. The probability of having an IQ score higher than 95 is 0.6306. c. Approximately 81.86% of the population have IQ scores between 70 and 130. d. The IQ score corresponding to the 88th percentile is approximately 116.055. 1. A z-score of 0 indicates an IQ score of 100.
Explanation:
a. To calculate the z-score when given an IQ score of 95, we can use the formula z = (x - μ) / σ. Plugging in the values, we get z = (95 - 100) / 15 which simplifies to z = -0.33.
b. To find the probability that a person will have an IQ score higher than 95, we need to calculate the area under the normal curve to the right of the z-score. We can use a z-table or a calculator to find this value. From the z-table, we find that the probability is approximately 0.6306.
c. To calculate the percentage of the population with IQ scores between 70 and 130, we can find the area under the normal curve between these two z-scores. Using a z-table or a calculator, we find that the area is approximately 0.8186 or 81.86%.
d. To find the IQ score corresponding to the 88th percentile, we need to find the z-score that corresponds to this percentile. Using a z-table or a calculator, we find that the z-score is approximately 1.137. We can then use the z-score formula to find the IQ score: x = z * σ + μ. Plugging in the values, we get x = 1.137 * 15 + 100, which simplifies to x = 116.055. Therefore, the IQ score corresponding to the 88th percentile is approximately 116.055.
1. A z-score of 0 indicates that the IQ is equal to the mean. Therefore, the IQ would be 100.
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