Question

In: Statistics and Probability

True or false 1. For healthy children (ages 5 to 15 years), the left atrial diameter...

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.

Solutions

Expert Solution

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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