Maths · Probability: Probability of an event, addition and multiplication theorems of probability
The scores on standardized admissions test are normally distributed with a mean
The scores on standardized admissions test are normally distributed with a mean of 500 and a standard deviation of \( 100 . \) What is the probability that a randomly selected student will score between 400 and 600 on the test?
- A. About \( 63 \% \)
- B. About \( 65 \% \)
- C. About \( 68 \% \)
- D. About \( 70 \% \)
Step-by-step solution
The scores follow a normal distribution with mean 500 and standard deviation 100. The interval 400 to 600 corresponds to ±1 standard deviation from the mean. For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Hence, the probability is about 68%.
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