Question

In: Statistics and Probability

Consider the approximately normal population of heights of male college students with mean μ = 64...

Consider the approximately normal population of heights of male college students with mean μ = 64 inches and standard deviation of σ = 4.6 inches. A random sample of 10 heights is obtained.

(a) Describe the distribution of x, height of male college students.

skewed leftapproximately normal    skewed rightchi-square


(b) Find the proportion of male college students whose height is greater than 74 inches. (Round your answer to four decimal places.)


(c) Describe the distribution of x, the mean of samples of size 10.

skewed rightapproximately normal    chi-squareskewed left


(d) Find the mean of the x distribution. (Round your answer to the nearest whole number.)


(ii) Find the standard error of the x distribution. (Round your answer to two decimal places.)


(e) Find P(x > 68). (Round your answer to four decimal places.)


(f) Find P(x < 63). (Round your answer to four decimal places.)

Solutions

Expert Solution

a) since, population is approx normal, so,  distribution of x, height of male college students will be approx normal

b)

µ =    64                  
σ =    4.6                  
                      
P ( X > 74   ) = P( (X-µ)/σ ≥ (74-64) / 4.6)              
= P(Z > 2.17   ) = P( Z <   -2.174   ) =    0.0149   (answer)

c) approximately normal

d) mean of the x distribution=64

ii)  standard error of the x distribution = std error = σ/√n=   1.45

e)

µ =    64                                      
σ =    4.6                                      
n=   10                                      
                                          
X =   68                                      
                                          
Z =   (X - µ )/(σ/√n) = (   68   -   64   ) / (    4.6   / √   10   ) =   2.750  
                                          
P(X ≥   68   ) = P(Z ≥   2.75   ) =   P ( Z <   -2.750   ) =    0.0030           (answer)

f)

µ =    64                                      
σ =    4.6                                      
n=   10                                      
                                          
X =   63                                      
                                          
Z =   (X - µ )/(σ/√n) = (   63   -   64.00   ) / (   4.600   / √   10   ) =   -0.687  
                                          
P(X < 63   ) = P(Z ≤   -0.687   ) =   0.2459                       (answer)


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