Question

Problem 1. Let x be a random variable which approximately follows a normal distribution with mean i = 1000 and o = 200. Use the z-table (attached to this test), calculator, or computer software to find the following: Part A. Find P(> 1500). Part B. Find P(x < 900). Part C. Find P(900<x<1500).

Answer 1

Given :

$\mu = 1000 , \sigma = 200$

Solution :

Part A)

$P(x > 1500) = P \left [ z > \frac{x - \mu }{\sigma } \right ]$

$P(x > 1500) = P \left [ z > \frac{1500 - 1000 }{200 } \right ]$

$P(x > 1500) =1 - P \left [ z < 2.5 \right ]$

... from Z table

Part B)

$P(x < 900) = P \left [ z < \frac{x - \mu }{\sigma } \right ]$

$P(x > 900) = P \left [ z < \frac{900 - 1000 }{200 } \right ]$

$P(x < 900) =P \left [ z < -0.5 \right ]$

... using Z table

Part C)

from Part A and Part B,

... using Z table

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