Kimsellers68idn
Answered

Discover a wealth of knowledge and get your questions answered at IDNLearn.com. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.

Assume the random variable X is normally distributed, with mean = 57 and standard deviation = 4. Find the 15th percentile. ​

Sagot :

LammettHashidn

The 15th percentile is the value x such that

P(X ≤ x) = 0.15

Let Z be a random variable following the standard normal distribution with mean 0 and standard deviation 1. Then

X = 57 + 4Z

or

Z = (X - 57)/4

so that

P((X - 57)/4 ≤ (x - 57)/4) = 0.15

P(Z ≤ (x - 57)/4) = 0.15

If F is the inverse CDF for the standard normal distribution, then

(x - 57)/4 = F(0.15) ≈ 0.5596

x - 57 ≈ 2.2385

x ≈ 59.2385

Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.