In: Statistics and Probability
True or false
1. For healthy children (ages 5 to 15 years), the left atrial diameter has a mean of μ = 26.4 millimeters and a standard deviation of σ = 4.2 millimeters. If a patient has a left atrial diameter of 31.7 millimeters, they would not fall in the top 10% of this population.
2. Almost three-fourths of US pecans are grown in the states of GA, NM, and TX. It is known that the average yield of pecans in Dona Ana County is μ = 1625 lbs/acre with a standard deviation of σ = 200 lbs/acre. Are the following statements true or false.
1. If a RANDOM SAMPLE of 18 acres of land is taken, the probability of the average yield of these 18 acres being at most 1700 lbs/acre would be .9441.
2. If the average yield from a RANDOM SAMPLE of 18 acres of land is 1700 lbs/acre, this sample average would fall above the 95th percentile of all such sample means.
1)
µ= 26.4
σ = 4.2
P(X≤x) = 0.9
Z value at 0.9 =
1.2816 (excel formula =NORMSINV(
0.9 ) )
z=(x-µ)/σ
so, X=zσ+µ= 1.282 *
4.2 + 26.4
X = 31.783
(answer)
TRUE
(f a patient has a left atrial diameter of 31.7
millimeters, they would not fall in the top 10% of this
population.)
.....
2)
a)
µ = 1625
400
σ = 200
n= 18
X = 1700
Z = (X - µ )/(σ/√n) = ( 1700
- 1625.00 ) / (
200.000 / √ 18 ) =
1.591
P(X ≤ 1700 ) = P(Z ≤
1.591 ) = 0.9441
excel formula for probability from z score is
=NORMSDIST(Z)
TRUE
.
B)
µ = 1625
σ = 200
n= 18
proportion= 0.9500
Z value at 0.95 =
1.645 (excel formula =NORMSINV(
0.95 ) )
z=(x-µ)/(σ/√n)
so, X=z * σ/√n +µ= 1.645 *
200 / √ 18 +
1625 = 1702.54
FALSE
........
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