The mean of a population is 74 and the standard deviation is 13. The shape of th

Question

The mean of a population is 74 and the standard deviation is 13. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. a. A random sample of size 32 yielding a sample mean of 79 or more b. A random sample of size 130 yielding a sample mean of between 72 and 76 c. A random sample of size 218 yielding a sample mean of less than 74.3 (Round all the values of z to 2 decimal places and final answers to 4 decimal places.) a. ____ b. ____ c. ____

Explanation / Answer

a|) for n=32;

std error of mean =std deviation/(n)1/2 =2.298

therefore P(X>79)=1-P(X<79)=1-P(Z<(79-74)/2.298)=1-P(Z<2.1757)=1-0.9852=0.0148

b) std error =1.140

P(72<X<76)=P(-1.7541<Z<1.7541)=0.9603-0.0397=0.9206

c)std error =0.8805

P(X<74.3)=P(Z<0.3407)=0.6333

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