Question

Need help with 19 and 20! Don’t understand

d. About how many students scored below 547 .025 X 120-3T 5467 18. Lengths of fish caught by 1200 30 a commercial fishing boat have a bell-shaped distribution with mean 23 inches 11 st 0 a4 About how many students scored below 54?.025 and standard deviation 1.5 inches. tion of all fish caught are between 20 inches and 26 inches long? 15.4 ,7 a. About what proportion of all fish b. About what proportion of all fish caught are between 20 inches and 23 inches long? :. About how long is the longest fish caught (only a small fraction of a percent are longer)? 19. Hockey pucks used in professional hockey games must weigh between 5,5 and 6 ounces. f the weight of 20 pucks manufactured by a particular process is bell- shaped, has mean 5.75 ounces and standard deviation 0.125 ounce, what proportion of the pucks will be usable in professional games? 20. Hockey pucks used in professional hockey games must weigh between 5.5 and 6 ounces. f the weight of pucks manufactured by a particular process is bell-shaped and has mean 5.75 ounces, how large can the standard deviation be if 99.7% of the pucks are to be usable in professional games? 22. Suppose that, as in the previous exercise, speeds of vehicles on a section of highway have mean 60 mph and standard deviation 2.5 mph, but now the distribution of speeds is unknown. a. If the speed limit is 55 mph, at least what proportion of vehicles must speeding? b. What can be said about the proportion of vehicles going 65 mph or faster? 23. An instructor announces to the class that the scores on a n mean 75 and standard deviation 5
Need it dumbed down

Answer 1

19)

µ =    5.75                              
σ =    0.1250                              
we need to calculate probability for ,                                  
5.5   ≤ X ≤    6                          
X1 =    5.5   ,   X2 =   6                  
                                  
Z1 =   (X1 - µ ) / σ =   -2.000                          
Z2 =   (X2 - µ ) / σ =   2.000                          
                                  
P (   5.5   < X <    6   ) =    P (    -2   < Z <    2.000   )
                                  
= P ( Z <    2.000   ) - P ( Z <   -2.000   ) =    0.9772   -    0.0228   =    0.9545(ANSWER)

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