The weights of bowling balls are normally distributed with mean 11.5 pounds in a

Question

The weights of bowling balls are normally distributed with mean 11.5 pounds in a standard deviation of 2.7 pounds a sample of 36 bowling balls selected what is the probability that the average weight of the sample is less than 11.25 pounds Answer Save uestion 3 (5 points) The weights of bowling balls are normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. A sample of 36 bowling balls is selected. What is the probability that the average weight of the sample is less than 11.25 pounds? Write only a number as your answer. Round to 4 decimal places (for example 0.0048). Do not write as a percentage. Your Answer: Answer Save

Explanation / Answer

mean= 11.5 pounds and std= 2.7 and n= 36

standard error= 2.7/sqrt(36)= 2.7/6= 0.45

the probability that the average weight of the sample is less than 11.25 pounds

Since =11.5 and (xbar)=0.45 we have:

P ( X<11.25 )=P ( X<11.2511.5 )=P ((X)/<(11.2511.5)/0.45)

Since (x)/=Z and (11.2511.5)/0.45=0.56 we have:

P (X<11.25)=P (Z<0.56)

Use the standard normal table to conclude that:

P (Z<0.56)=0.2877

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