Download Quiz 4 Answer Key

STAT 2601 QUIZ #4
NAME:
Student ID:
Problem1. Suppose we consider the time it takes to drive
from the university campus to downtown at a major
metropolitan at 5::00 PM on weekends. We believe the
distribution is approximately normal with a mean of 42
minutes and a standard deviation of four minutes. What
proportion of the drive times will take between 36.8 and 38
minutes? (2 pts)
(Answer) Since
  42 and   4 ,
P(36.8  X  38)
36.8  42
38  42
 P(
Z
)
4
4
 P(1.3  Z  1.0)
 P(1.0  Z  1.3)  0.4032  0.3413
 0.0619
Problem 2. Supose x is a uniform random variable with c=40
and d=50. Find the probability that a randomly selected
observation exceeds 42? (2 pts)
(Answer) Since f(x)= 1/(d-c)=1/(50-40)=0.1,
P(X > 42) = (50-42)f(x)=0.8.
Problem 3. The amount of corn chips dispensed into a 10ounce bag by the dispensing machine has been identified at
possessing a normal distribution with a mean of 10.5 ounces
and a standard deviation of 0.2 ounces. Suppose 100 bags
of chips were randomly selected from this dispensing
machine. Find the probability that the sample mean weight of
these 100 bags exceeds 10.6 ounces? (3 pts)
(Answer) Since
  10.5,   .2 , and n=100,
0.2
 0.02
 x    10.5 and  x 
100
X   x 10.6  10.5

)
P( X  10.6)  P(
x
0.02
 P( Z  5)  0.0000
Problem 4. The average score of all pro golfers for a
particular course has a mean of 70 and a standard deviation
of 3.0. Suppose 36 golfers played the course today. Find the
probability that the average score of the 36 golfers exceeded
71? (3 pts)
(Answer) Since
  70 ,   3, and n=36,
3
 0. 5
36
X   x 71  70

)
P( X  10.6)  P(
x
0.5
 P( Z  2.0)  0.5  P(0  Z  2.0)
 x    70 and  x 
= 0.5 – 0.4772=0.0228.