Question

1) Given a standard normal distribution, find the probability of having a z score higher than 1.67

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2) Given that test scores for a class are normally distributed with a mean of 80 and variance 36, find the probability that a test score is lower than a 45.
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3) Given a standard normal distribution, find the Z score associated with a probability of .888
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4) Find the Z score associated with the 33rd quantile of a normal distribution with mean 42 and standard deviation of 4
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5) Given a sample of values that approximately follows the normal distribution with mean 1300 and standard deviation 105, find the probability that a given value is between 1000 and 1225
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6) Find the probability that a value from a standard normal distribution is between -3 and 3.

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7) Given a standard normal distribution where P(A<Z<1.35)=.38, find A.

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8) Find the value associated with the 64th quantile of the data from an approximate normal distribution with mean 17 and standard deviation 3.7.

Please Solve using Rstudio codes and thanks

Answer 1

R code along with output is attached herewith.

#1) pnorm(1.67) ## [1] 0.9525403 #2) pnorm(45, 80, 6) ## [1] 2.716544e-09 #3) qnorm(0.888) ## [1] 1.21596 #4) qnorm(0.33, 42, 4) ## [1] 40.24035 #5) pnorm(1225, 1300, 105) - pnorm(1000, 1300, 105) ## [1] 0.2353879 #6) pnorm(3) - pnorm(-3) ## [1] 0.9973002 #7) #Here we need to find A such that P(A<Z<1.35) = 0.38 #P(Z<1.35) - P(Z<A) = 0.38 #P(Z<1.35) - 0.38 = P(Z<A) pnorm(1.35) - 0.38

## [1] 0.531492 #which implies that we need to find A such that #P(Z<A) = 0.531492 qnorm(0.531492) ## [1] 0.0790209 #S0 A = 0.0790209 #8) qnorm(0.64, 17, 3.7) ## [1] 18.3263

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Thankyou.