Lecture04

# Lecture04 - STAT 350 LECTURE 4 ANNOUNCEMENT Lab 1 due by...

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STAT 350 L ECTURE 4

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A NNOUNCEMENT Lab 1 due by midnight today. Lab Help Session Today: 3:30 PM – 4:30 PM @ ENAD 240 Homework #2 due Friday Jan 28 To be posted on the blackboard soon…
H OW T O F IND P ROBABILITY FOR ANY NORMAL DISTRIBUTION Density function for a normal distribution:

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H OW T O F IND P ROBABILITY FOR ANY NORMAL DISTRIBUTION Step 1: Z-transformation: convert it to a standard normal z: standardized value of x ( z -score) Step 2: Look up the probability of the corresponding z-score on the Z-table Read the Proposition on page 38
E XAMPLE 1.16 The time that it takes a driver to react to the brake light on a decelerating vehicle is critical in avoiding rear-end collisions. The reaction tiem for an in-traffic response to a brake signal from standard brake lights can be modeled with a normal distribution having parameters = 1.25 sec and = 0.46 sec. In the long run, what proportion of reaction time will be between 1.00 sec and 1.75 sec? Solution: Let x denote the reaction time in seconds.

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P ERCENTILE P ROBLEMS FOR N ORMAL D ISTRIBUTION Scores on the SAT Verbal test in recent years follow approximately the N(505, 110) distribution. How high must a student score in order to place in the top 10% of all students taking the SAT?
E XAMPLE -- I NVERSE N ORMAL C ALCULATIONS Scores on the SAT Verbal test in recent years follow approximately the N(505, 110) distribution. How high must a student score in order to place in the top 10% of all students taking the SAT? Solution: Step 1: find the z-score corresponds to 90 th percentile Z = 1.28 z=1.28 is the standardized value with area 0.9 to its left

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E XAMPLE -- I NVERSE N ORMAL C ALCULATIONS Scores on the SAT Verbal test in recent years follow approximately the N(505, 110) distribution. How high must a student score in order to place in the top 10% of all students taking the SAT?
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