Find the x value to the right of the mean such that 85% of the total area under

Question

Find the x value to the right of the mean such that 85% of the total area under the standard normal distribution curve lies to the left of it? Mrs. Smith's reading class can read an average of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would need to read in order to get the award? Assume the data is normally distributed. At a large department store, the average number of years of employment for a is 5.7 with a standard deviation of 1.8 years, and the distribution is approximately normal. If an employee is picked at random, what is the probability that the employee has worked at the store for over 10 years?

Explanation / Answer

1. That question means that clculate the value of Z for which probability is 0.85

so Pr(X<=x; ; ) = 0.85

so related Z - value from Z - table = 1.04

so answer is 1.04

2. Here top 3% will receive award that means these top 3% people have to write words more than other 97% students.

Pr( Number of words>x; 175; 20) = 0.03

so Pr( Number of words<x; 175; 20) = 0.97

calculating respective value of Z from the Z - table for probability = 0.97

Z= 1.88

Here Z = (x - 175)/ 20 = 1.88

x = 175 + 20 * 1.88 = 212.6 words

3. Here mena year of experience = 5.7

standard deviation = 1.8 years

so let say X is the number of experience and it has normal distribution

so, Pr(X >=10 ; 5.7; 1.6) = 1 - Pr(X<10 ; 5.7; 1.6)

we will calculate z - value first Z = (x- 5.7)/1.6 = (10-5.7)/1.6 = 2.6875

so respective p- value from Z - table = 0.9964

so Pr(X >=10 ; 5.7; 1.6) = 1-0.9964 = 0.0036

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