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# A normally distributed random variable X has a mean of 90. Given that the probability $\mathrm{P}(X<85) \approx 0.16 :$ a. find the proportion of scores between 90 and 95, i.e., find P(90 < X < 95) b. find an estimate of the standard deviation for the random variable X.

Solution

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$\textbf{Part a}$

To solve this part of the exercise, we must remember that the graph of the probability density function for the normal distribution is symmetrical about $x = \mu$.

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