The compressive strength of samples of cement can be modeled by a normal distribution with a mean of 6000 kilograms per square centimeter and a standard deviation of 100 kilograms per square centimeter. (a) What is the probability that a samples strength is less than 6250 kilograms per square centimeter? (b) What is the probability that a samples strength is between 5800 and 5900 kilograms per square centimeter? (c) What strength is exceeded by 95% of the samples?

Answer

a

b

c

Question

From the question we are told that

   The mean is  

    The standard deviation is  

Generally the probability that a samples strength is less than 6250 kilograms per square centimeter is mathematically represented as

Generally

From the z-table  

Generally the probability that a samples strength is between 5800 and 5900 kilograms per square centimeter is mathematically represented as

=>

=>  

From the z-table  

and

So

=>      

Generally the strength that is exceeded by 95% is mathematically evaluated  as

=>

From the normal distribution table  the critical value  of  0.05 is  

So

=>  

=>  

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step-by-step explanation:

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