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Black_prince [1.1K]
3 years ago
15

Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What perce

nt of people who write this exam obtain scores between 350 and 650?
Mathematics
1 answer:
Alla [95]3 years ago
3 0

Answer:

The percentage is P(350 <  X  650 ) = 86.6\%

Step-by-step explanation:

From the question we are told that

   The population mean is  \mu  =  500

     The standard deviation is  \sigma  =  100

The  percent of people who write this exam obtain scores between 350 and 650    

    P(350 <  X  650 ) =  P(\frac{ 350 -  500}{ 100}

Generally  

               \frac{X -  \mu }{\sigma }  =  Z (The \  standardized \  value \ of  \  X )

   P(350 <  X  650 ) =  P(\frac{ 350 -  500}{ 100}

   P(350 <  X  650 ) =  P(-1.5

   P(350 <  X  650 ) =  P(Z < 1.5) -  P(Z <  -1.5)

From the z-table  P(Z <  -1.5 )  =  0.066807

   and P(Z < 1.5  ) =  0.93319

=>    P(350 <  X  650 ) =  0.93319 -  0.066807

=>  P(350 <  X  650 ) = 0.866

Therefore the percentage is  P(350 <  X  650 ) = 86.6\%

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