Question

QUESTION 11 Use your TI83 (or Excel): A normally distributed population has a mean of 77 and a standard deviation of 15. Determine the probability that a random data has a value of less than 74. Round to four decimal places.

QUESTION 12 Use your TI83 (or Excel): A normally distributed population has a mean of 77 and a standard deviation of 12. Determine the probability that a random data has a value between 72 and 80. Round to four decimal places.

QUESTION 13 Use your TI83 (or Excel): A normally distributed population has a mean of 74 and a standard deviation of 18. Determine the probability that a random data has a value between 71 and 82. Round to four decimal places.

QUESTION 14 Use your TI83 (or Excel): A normally distributed population has a mean of 72 and a standard deviation of 20. Determine the probability that a random data has a value between 74 and 81. Round to four decimal places.

QUESTION 15 Use your TI83 (or Excel): A normally distributed population has a mean of 79 and a standard deviation of 14. Determine the probability that a random data has a value of less than 77. Round to four decimal places.

Answer 1

USING EXCEL

We can find above probabilities using excel function NORMDIST(x, mean, standard deviation, cumulative)

cumulative= True

this function gives the CDF or cumulative distribution function of a normal distribution with specified mean and standard deviation i.e., P(X<x) where X is a normal distributed Random variable

or in other words, when cumulative is true this function gives Probability of X  from -infinity (lower limit of normal distribution) to x i.e., P(-inf<X<x)=P(X<x)

11

12,

13.

14.

15.