A stockbroker has kept a daily record of the value of a particular stock over th

Question

A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. 1. Refer to Exhibit 5-1.The percentile rank of a price of $13.87 is _____ a. 48.78% b. 1.22% c. 98.78% d. 51.22% Refer to Exhibit 5-1. The stock price beyond which 0.05 of the distribution falls is _____. a. $4.60 b. $12.47 c. $4.57 d. $12.44 A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 a standard deviation of 90. The scores are normally distributed. Refer to Exhibit 5-2. The proportion of scores that lie above 650 is _____. a. 0.4535 b. 0.9535 c. 0.0475 d. 0.0485 Refer to Exhibit 5-2. The proportion of scores that lie between 460 and 600 is _____. a. 0.4394 b. 0.5365 c. 0.4406 d. 0.4635 5. Refer to Exhibit 5-2. The raw score that lies at the 90th percentile is _____. a. 615.20 b. 384.80 c. 616.

Explanation / Answer

Solving question 1 , we use z tables to calculate probability and vice-versa

For part a,

Z = (x-u)/sigma = (13.87-8.52) / 2.38 = 2.24,

Using normal tables one sided for z = 2.24, we get probability value and percentile rank as 98.78%

Similarly, for part b,

We want to know z value in one-sided normal distribution for which cumulative probability is 95% .

Hence, z = 1.644853

z = (x-u)/sigma

Now, x = 1.644853 * 2.38 + 8.52 = 12.44 Hence,answer is D

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