1. Find the following probabilities. Sketch the corresponding area. (4 points) a

Question

1. Find the following probabilities. Sketch the corresponding area. (4 points) a. P (0 Z .5)= b. P (Z .5)= c. P (Z -.5) d. P (Z .5) e. P (-.5 Z .5) 2. Find the value of z for the following probability statements, and sketch the corresponding area. (4 points) a. P (0 Z z) = .4901 b. P (z Z 0) = .2324 c. P (Z z) = .8888 d. P (Z z) = .2090 e. P (Z z) = .7910 3. The estimated miles-per-gallon (on the highway) ratings of a class of trucks are normally distributed with a mean of 12.8 and a standard deviation of 3.2. What is the probability that one of these trucks selected at random would get (2 points) a. between 13 and 15 miles per gallon? b. between 10 and 12 miles per gallon?

Explanation / Answer

Solution:-

The estimated miles-per-gallon (on the highway) ratings of a class of trucks are normally distributed with a mean of 12.8 and a standard deviation of 3.2.

a) The probability that one of these trucks selected at random would get between 13 and 15 miles per gallon is 0.2289.

x1 = 13

x2 = 15

By applying normal distrinbution:-

z = (x - u)/S.D

z(x1 = 13) = 0.0625

z(x2 = 15) = 0.6875

P(0.0625 < z < 0.6875) = P(z > 0.0625) - P(z > 0.6875)

P(0.0625 < z < 0.6875) = 0.474 - 0.2451

P(0.0625 < z < 0.6875) = 0.2289

b) The probability that one of these trucks selected at random would get between 10 and 12 miles per gallon is 0.2088.

x1 = 10

x2 = 12

By applying normal distrinbution:-

z = (x - u)/S.D

z(x1 = 10) = - 0.875

z(x2 = 12) = -0.25

P(- 0.875 < z < - 0.25) = P(z > - 0.875) - P(z > - 0.25)

P(- 0.875 < z < - 0.25) = 0.8075 - 0.5987

P(- 0.875 < z < - 0.25) = 0.2088

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