Question

A psychologist was particularly interested in the relationship between hypnosis on memory. To test this she exposed 10 subjects to a list of 40 nonsense words. She then hypnotized each subject and asked them to recall as many words from the list as was possible. The mean of these responses is 22 and the standard deviation is 5.9.

1. LV remembered 0 words. What is their z score?
2. SI remembered 21 words. What is their T score?
3. What proportion of subjects remembered less than 11 words?
4. What proportion of subjects remembered more than 13 words?
5. What proportion of subjects remembered less than 28 words?
6. What proportion of subjects remembered between 16 and 20 words?
7. How many words would you have remembered if only 20% of the subjects remembered less than you?

Answer 1

A)

Z=(X-µ)/σ= (0-22)/5.9=       -3.73

B)

µ=   22.00  
σ=   1.865743819  

X=   21  
t score=(X-µ)/σ= (21-22)/1.86574381949934=       -0.54

C)

Less than 11 words

µ =    22      
σ =    5.9      
          
P( X ≤    11   ) = P( (X-µ)/σ ≤ (11-22) /5.9)  
=P(Z ≤   -1.86   ) =   0.03113

d)

µ =    22                  
σ =    5.9                  
                      
P ( X ≥   13   ) = P( (X-µ)/σ ≥ (13-22) / 5.9)              
= P(Z ≥   -1.53   ) = P( Z <   1.525   ) =    0.9364   (answer)

e)

µ =    22      
σ =    5.9      
          
P( X ≤    28   ) = P( (X-µ)/σ ≤ (28-22) /5.9)  
=P(Z ≤   1.02   ) =   0.84541

f)

µ =    22          
σ =    5.9          
we need to calculate probability for ,              
P (   16   < X <   20   )
=P( (16-22)/5.9 < (X-µ)/σ < (20-22)/5.9 )              
              
P (    -1.017   < Z <    -0.339   )
= P ( Z <    -0.339   ) - P ( Z <   -1.02   ) =
0.3673   -    0.1546   =    0.2127

g)

µ=   22  
σ =    5.9  
P(X≤x) =   0.2  
      
z value at 0.2=   -0.8416   (excel formula =NORMSINV(0.2))
z=(x-µ)/σ      
so, X=zσ+µ=   -0.842   *5.9+22
X =   17.034   (answer)

Please let me know in case of any doubt.

Thanks in advance!

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