# Probability Distribution in Research/Main

A machine is set to fill a bottle with 8 grams of medicine. A sample of 8 recently filled bottles revealed the following grams of medicine: 9.2, 8.7, 8.9, 8.4, 8.3, 8.5, 8.1, 8. Using a One Sample t Test, answer the following questions 4-9.

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#### Solution Preview

Please see the attached file.

Be sure you can use Excel's Data Analysis for this exam. The ANSWER line should expand to accommodate your answer. Keep your answers as short as possible. Where appropriate, always use an alpha of .05, always use the one tail test, always use a confidence interval of 95%, and assume Z = 1.96 in formulas for confidence interval calculations and sample size calculations.

1. = 250, s = 62. Probability of X being 260 or more equals:

z = (260-250)/ 62

= 0.1613

From the z-score tables, we can see that the probability corresponding to z = 0.1613 is 0.5640

Hence, the probability that the score above 190 is

= 1 - 0.5640

= 0.4359

ANSWER: 0.4359

2. = 250, s = 62, n = 24. The 95% confidence interval for µ equals:

C.I. = ± z*s/sqrt(n)

= 250 ± 1.96*62/sqrt(24)

= (225.19, 274.80)

ANSWER: (225.19, 274.80)

3. = 250, s = 62, n = ...

#### Solution Summary

The solution uses one sample t test to determine the probability distribution.