Question

8) A psychological experiment finds that all paranoid schitzophrenics have eye contact

               times in the bottom 10 percent. Find the cutoff score for them if the average eye

               contact time is 200 seconds and the standard deviation is 35 seconds.

               a) 20            b) 39               c) 69.8            d) 155               e) 200

9) If the chance of getting a broken cookie is .05, what is the probability of getting two

               or more broken cookies in a bag of 40 cookies? Use correction for continuity.

               a) .74           b) .358           c) .64             d) .09             e) .19

10) The mean blood glucose level in adults is 85 with a standard deviation of 25. What is

                 the probability of finding a three reading average greater than 100?

                  a) .1493                b) .274             c) .0228             d) .04               e) .360

11) The National Center for Educational Statistics surveyed 5400 college graduates about

                 the lengths of time required to earn their bachelors degrees. The mean is 5.4 years and

                 the standard deviation is 1.9 years. Based on this sample, construct a 90% confidence

                 interval for the mean time required by all college graduates

                 a) 4.09-4.22           b) 5.36 - 5.44             c) 5.74-5.96          d) 4.37-6.06

12) Given that the average shower time at a hotel is 11.4 minutes with a standard deviation    

                 of 7 minutes, what is the probability that a group of 20 guests will shower on average

                 between 11.5 and 11.6 minutes?

                a) .10               b) .42              c) .1253             d) .20           e) .0253

Answer 1

8)

µ=   200                  
σ =    35                  
proportion=   0.1                  
                      
Z value at    0.1   =   -1.28   (excel formula =NORMSINV(   0.1   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   -1.28   *   35   +   200

X   =   155.   

9)

Sample size , n =    40                      
Probability of an event of interest, p =   0.05                      
right tailed                          
X ≥   2                      
                          
Mean = np =    2                      
std dev ,σ=√np(1-p)=   1.3784                      
                          
P(X ≥   2   ) = P(Xnormal ≥   1.5   )          
                          
Z=(Xnormal - µ ) / σ = (   1.5   -   2   ) /   1.3784   =   -0.363
                          
=P(Z ≥   -0.363   ) =    0.64

10)

µ =    85                  
σ =    25                  
                      
P ( X ≥   100.00   ) = P( (X-µ)/σ ≥ (100-85) / 25)              
= P(Z ≥   0.600   ) = P( Z <   -0.600   ) =    0.274

11)

Level of Significance ,    α =    0.1          
degree of freedom=   DF=n-1=   5399          
't value='   tα/2=   1.6451   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   1.9000   / √   5400   =   0.025856
margin of error , E=t*SE =   1.6451   *   0.02586   =   0.042536
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    5.40   -   0.042536   =   5.357464
Interval Upper Limit = x̅ + E =    5.40   -   0.042536   =   5.442536
90%   confidence interval is (   5.36   < µ <   5.44   )

12)

µ =    11.4                                  
σ =    7                                  
n=   20                                  
we need to calculate probability for ,                                      
11.5   ≤ X ≤    11.6                              
X1 =    11.5   ,    X2 =   11.6                      
                                      
Z1 =   (X1 - µ )/(σ/√n) = (   11.5   -   11.4   ) / (   7   / √   20   ) =   0.06
Z2 =   (X2 - µ )/(σ/√n) = (   11.6   -   11.4   ) / (   7   / √   20   ) =   0.13
                                      
P (   11.5   < X <    11.6   ) =    P (    0.1   < Z <    0.1   )   
                                      
= P ( Z <    0.13   ) - P ( Z <   0.06   ) =    0.55084   -    0.52547   =    0.0253   

Thanks in advance!

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