Question

The weights of ripe watermelons grown at a farm are normally distributed with a mean of 12.2 pounds and a standard deviation of 1.2 pounds.

1. What is the probability that a watermelon weighs more than 13.5 pounds? (round to 3 decimal places)  
2. What is the probability that a watermelon weighs less than 12 pounds? (round to 3 decimal places)  
3. What is the probability that a watermelon weighs between 11.3 and 12 pounds? (round to 3 decimal places)  
4. What is the minimum height a tulip can be and still be in the heaviest 8% of watermelons? (round to 1 decimal place)  

What did you use to answer this question, the tables or the calculator? Make sure your work confirms your answer.  

Answer 1

a)

µ =    12.2                  
σ =    1.2                  
                      
P ( X ≥   13.5   ) = P( (X-µ)/σ ≥ (13.5-12.2) / 1.2)              
= P(Z ≥   1.08   ) = P( Z <   -1.083   ) =    0.1393   (answer)

b)

P( X ≤    12   ) = P( (X-µ)/σ ≤ (12-12.2) /1.2)      
=P(Z ≤   -0.17   ) =   0.4338   (answer)

c)

we need to calculate probability for ,                                      
P (   11.3   < X <   12   )                      
=P( (11.3-12.2)/1.2 < (X-µ)/σ < (12-12.2)/1.2 )                                      
                                      
P (    -0.750   < Z <    -0.167   )                       
= P ( Z <    -0.167   ) - P ( Z <   -0.75   ) =    0.4338   -    0.2266   =    0.2072   (answer)

d)

P(X≤x) =   0.92                  
                      
Z value at    0.92   =   1.4051   (excel formula =NORMSINV(   0.92   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   1.405   *   1.2   +   12.2  
X   =   13.9   (answer)