Answer :
The correct options are (f) and (b). Students at Arrowhead High School took an English test with a mean of 120 and a standard deviation of 25. Approximately, 95% of the IQ scores are between 70 and 170 .
To determine the range where approximately 95% of the scores fall, we apply the Empirical Rule (68-95-99.7 rule) in a normal distribution. According to this rule, about 95% of the data lies within two standard deviations from the mean.
Given:
Mean = 120
Standard Deviation = 25
Range calculation:
Lower Bound = Mean - 2 * Standard Deviation
Upper Bound = Mean + 2 * Standard Deviation
Lower Bound = 120 - 2 * 25 = 120 - 50 = 70
Upper Bound = 120 + 2 * 25 = 120 + 50 = 170
Therefore, approximately 95% of the IQ scores are between 70 and 170.
From the options provided: a. 145 b. 170 c. 85 d. 95 e. 115 f. 70, the correct options are 70 and 170.
