Download Assignment 7 –key 6.51 (a) PHStat output: Probability for X > X

Assignment 7 –key
6.51
(a)
PHStat output:
Probability for X >
X Value
Z Value
P(X>0)
(b)
0
1.925
0.0271
P(X > 0) = P(Z > 1.925) = 0.0271
PHStat output:
Probability for X >
X Value
Z Value
P(X>10)
10
2.425
0.0077
P(X > 10) = P(Z > 2.425) = 0.0077
(c)
Probability for X <=
X Value
Z Value
P(X<=-50)
-50
-0.575
0.2826456
P(X < -50) = P(Z < -0.575) = 0.2826
(d)
Probability for X <=
X Value
Z Value
P(X<=-60)
-60
-1.075
0.1411874
P(X < -60) = P(Z < -1.075) = 0.1412
(e)
(a)
Probability for X >
X Value
Z Value
P(X>0)
(b)
0
1.35
0.0885
P(X > 0) = P(Z > 1.35) = 0.0885
PHStat output:
Probability for X >
X Value
Z Value
P(X>10)
10
1.6833333
0.0462
P(X > 10) = P(Z > 1.6833) = 0.0462
(c)
Probability for X <=
X Value
Z Value
P(X<=-50)
-50
-0.316667
0.3757483
P(X < -50) = P(Z < -0.3167) = 0.3757
(d)
Probability for X <=
X Value
Z Value
P(X<=-60)
-60
-0.65
0.2578461
P(X < -60) = P(Z < -0.65) = 0.2578
7.20
(a)
(b)
(c)
When n = 2 , the shape of the sampling distribution of X should closely resemble the
shape of the distribution of the population from which the sample is selected. Because the
mean is larger than the median, the distribution of the sales price of new houses is
skewed to the right, and so is the sampling distribution of X although it will be less
skewed than the population..
If you select samples of n = 100, the shape of the sampling distribution of the sample
mean will be very close to a normal distribution with a mean of $274,300 and a standard
deviation of
= $9,000.
X =

n

90000
100
 9000
PHStat output:
Common Data
Mean
Standard Deviation
Probability for X <=
X Value
Z Value
P(X<=300000)
(d)
274300
9000
300000
2.8555556
0.9978519
P( X < 300,000) = P(Z < 2.8556) = 0.9979
PHStat output:
Probability for a Range
From X Value
To X Value
Z Value for 275000
Z Value for 290000
P(X<=275000)
P(X<=290000)
P(275000<=X<=290000)
275000
290000
0.077778
1.744444
0.5310
0.9595
0.4285
P(275,000 < X < 290,000) = P(0.5310 < Z < 0.9595) = 0.4285