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# Multiple choice: Normal distribution, Confidence Interval

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1. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with m = 110 grams and Q(standard deviation)= 25 grams. A sample of 25 vitamins is to be selected. So, the middle 70% of all sample means will fall between what two values?
a) 104.8 and 115.2
b) 108.4 and 112.5
c) 115 and 100.7
d) 85 and 125

2. Which of the following about the normal distribution is not true?
a) Theoretically, the mean, median, and mode are the same.
b) About 2/3 of the observations fall within +,-1 standard deviation from the mean.
c) It is a discrete probability distribution.
d) Its parameters are the mean, m, and standard deviation, Q .

3. A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall.
Fifteen credit card accounts were randomly sampled and analyzed with the following results: X(sample mean)=\$50.50 and S square=400. Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall.
a) \$50.50+,- \$9.09
b) \$50.50+,- \$10.12
c) \$50.50+,- \$11.00
d) \$50.50+,- \$11.08

I need detail explanation

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#### Solution Preview

1. The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with m = 110 grams and Q(standard deviation)= 25 grams. A sample of 25 vitamins is to be selected. So, the middle 70% of all sample means will fall between what two values?
a) 104.8 and 115.2
b) 108.4 and 112.5
c) 115 and 100.7
d) 85 and 125

Answer: a) 104.8 and 115.2
70% Confidence limits

We use z distribution as population standard deviation is given

Mean=&#956;= 110 garams
Standard deviation =&#963;= 25 garams
sample size=n= 25
&#963;x=standard error of mean=&#963;/&#8730;n= 5 = ( 25 /&#8730; 25)
Confidence level= 70%
Therefore Significance level=&#945;= 30% =100% -70%
No of tails= 2
This is a 2 tailed test because we are calculating the confidence interval

Z at ...

#### Solution Summary

Three Multiple choice questions on Normal distribution, Confidence Interval are answered.

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