The TI-83/84 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(100,15,50) generates 50 values from a normally distributed population with and . One such generated sample of 50 values has a mean of 98.4 and a SD of 16.3. Assume that is known to be 15. Estimate the mean value from the random number generator using 99% confidence

99% confidence interval for the mean value from the random number generator is a lower limit of 85.87 and an upper limit of 110.93.

Step-by-step explanation:

Confidence interval = mean +/- margin of error (E)

mean = 98.4

sd = 16.3

n = 15

degree of freedom (df) = n - 1 = 15 - 1 = 14

confidence level (C) = 99% = 0.99

significance level = 1 - C = 1 - 0.99 = 0.01 = 1%

t-value corresponding to 14 df and 1% significance level is 2.977.

E = t×sd/√n = 2.977×16.3/√15 = 12.53

Lower limit = mean - E = 98.4 - 12.53 = 85.87

Upper limit = mean + E = 98.4 + 12.53 = 110.93

99% confidence interval for the mean is between 85.87 and 110.93

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