I need only (F) I need only (F) (a) Since X follows normal density curve so foll

Question

I need only (F)

I need only (F)

(a)

Since X follows normal density curve so following is the graph of the curve:

(b)

z-score for X=3000 is

z-score for X=4500 is

So the required probability is

Since normal distibution is continuous so probbaility at a particular point is zero. So we have

(c)

z-score for X=2500 is

The required probability is

(d)

z-score for X=6000 is

The required probability is

(e)

Here we need z-score that has 0.001 area to its right. From z-table, z-score 3.1 have 0.999 area to its left, that is 0.001 area to its right. So required X will be

Someone answered my question without (F)

Thus, I need the answer only part (f)

Let X be the birth weight, in grams, of a randomly selected full-term baby. The article "Fetal Growth Parameters and Birth Weight: Their Relationship to Neonatal Body Composition (Ultrasound in Obstetrics and Gynecology, 2009: 441446) suggests that X is normally distributed with mean 3500 and standard deviation 600. (a) Sketch the relevant density curve, including tick marks on the horizontal scale. b) What is P(3000 X

Explanation / Answer

f)

As u = mean = 3500 g, sigma = 600 g, and 1 g = 0.00220462 lbs, then converting,

u = mean = 3500*0.00220462 lbs = 7.71617 lbs
sigma = 600*0.00220462 = 1.322772 lbs

Now, for the critical value,

x = 2500*0.00220462 lbs = 5.51155 lbs

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    5.51155      
u = mean =    7.71617      
          
s = standard deviation =    1.322772      
          
Thus,          
          
z = (x - u) / s =    -1.666666667      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.666666667   ) =    0.047790352 [ANSWER]

As we can see, the answer is the same, even after conversion.

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