Answer :
To find the z-score for Jan's IQ of 89, we can use the formula: z = (x - mean) / standard deviation. Plugging in the values, we get: z = (89 - 99.8) / 15.3 = -0.706. The z-score represents the number of standard deviations Jan's IQ score is from the mean.
To find the z-score for Jan's IQ of 89, we can use the formula: z = (x - mean) / standard deviation. Plugging in the values, we get: z = (89 - 99.8) / 15.3 = -0.706. The z-score represents the number of standard deviations Jan's IQ score is from the mean.
For the second part of the question, since the z-score for Jan's IQ of 89 is negative, it means Jan's IQ is below the mean. We can use a z-table or a z-score calculator to find the probability associated with the z-score. In this case, the probability is approximately 0.2419 or 24.19%.
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The complete question is,
13. A random sample of IQ tests is normally distributed with a mean of 99.8 and a standard deviation of 15.3. Jan has an IQ of 89. Use this information to answer the following Z-score questions. a) Calculate the Z-score for Jan's' IQ. b) Write a sentence to explain the Z-score in context. c) Is Jan's' IQ unusually low compared to other people in the data set? Explain your answer.
