6.2.3 A random variable follows the normal probability distribution with a mean

Question

6.2.3 A random variable follows the normal probability distribution with a mean of 100 and a standard deviation of 10. Determine the probability for a randomly selected value from this population in parts a through d below a. What is the probability that the value is less than 80? The probability that the value is less than 80 is 0.0228 Round to four decimal places as needed.) b. What is the probability that the value is less than 70? The probability that the value is less than 70 is 0014 Round to four decimal places as needed.) c. What is the probability that the value is more than 105? The probability that the value is more than 105 is .3085 Round to four decimal places as needed.) d. What is the probability that the value is more than 751 The probability that the value is more than 75 is Round to four decimal places as needed.)

Explanation / Answer

solution=

random variable follows normal distribution
mean =100
standard deviation=10
a)p(x<80)
formula of z score
z=x bar-mean /standarddeviation
z= 80-100 /10
z=-2
p(x<80)=p(z<-2.0) = 1?0.9772=0.0228 (from z table)

b)p(x<70)

formula of z score
z=x bar-mean /standarddeviation
z= 70-100 /10
z=-3
p(x<70)=p(z<-3.0) = 1?0.9987=0.0013 (from z table)

c)p(x>105)

formula of z score
z=x bar-mean /standarddeviation
z= 105 -100 /10
z=0.5
p(x>105)=p(z >0.5) =1?P ( Z<0.5 )=1?0.6915=0.3085 (from z table)

d)P(X>75)

formula of z score
z=x bar-mean /standarddeviation
z= 75-100 /10
z=-2.5
p(x<75)=p(z<-2.5) =0.9938 (from z table)

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