Someone can help me to figure out these Math question. Appreciated!!!!!! The Nat

Question

Someone can help me to figure out these Math question. Appreciated!!!!!!

The National Health Statistics Reports dated Oct. 22, 2008, stated that for a sample size of 277 18-year-old American males, the sample mean waist circumference was 86.3 cm. Suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. How likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? Consider a binomial experiment with 100 trials of success probability 0.60. Use the central limit theorem to calculate the probability that the total number of successes is greater than 50.

Explanation / Answer

2.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    86.3      
u = mean =    85      
n = sample size =    277      
s = standard deviation =    15      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.442420805      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.442420805   ) =    0.074591849 [ANSWER]

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