The mass of white lab rats is known to be normally distributed with a mean of =
ID: 3172492 • Letter: T
Question
The mass of white lab rats is known to be normally distributed with a mean of = 20 grams and a standard deviation of = 1.6 grams.
3. Suppose that 9 white lab rats are selected at random and weighed together. What is the probability that the total mass of this sample will be below 184 grams?
(A) 0.0 (B) 0.1 (C) 0.2 (D) 0.3 (E) 0.4 (F) 0.5 (G) 0.6 (H) 0.7 (I) 0.8 (J) 0.9
4. The lifespans of light-emitting diodes are known to be exponentially distributed, with a mean lifespan of 12 years.
What is the 75th percentile? That is, what is the value of such that 75% of all diodes have a lifespan less than ?
(A) 12 (B) 12.5 (C) 13 (D) 13.5 (E) 14 (F) 14.5 (G) 15 (H) 15.5 (I) 16 (J) 16.5
Explanation / Answer
3. From information given, mu=20, and sigma=1.6, substitute the values in following Z score formula to compute the Z score and then find the area corresponding to the Z score.
P(X<20.44) [Total mass of 9 lab rats is 184 grams, therefore, average weight of lab rats is 20.44 (184/9)]
=P[Z<(20.44-20)/1.6] [Z=(X-mu)/sigma, where, X is raw score, mu is population mean and sigma is population standard deviation]
=P(Z<0.28)
=0.6103~0.6 (G)
4. Percentile, k=Ln(1-area to the left)/-m, where, Ln denotes natural log, and m=1/mu.
=Ln(1-0.75)/(-1/12)
=16.63 (J)
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