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# Statistics: 95% Confidence Intervals

1. The recommended retail price of a popular new midsize SUV is \$30,985. The price of the SUV in a sample of 30 deaerships in on average \$27,895 with a standard deviation of \$1,150. If this is a random sample and the price can be assumed to be normally distributed, construct a 95% confidence interval of the average sale price for the SUV.

2. A toy company wants to determine the average amount of time it takes an adult to assemble a highly popular "easy to assemble " toy. A sample of 21 yielded an average time of 21.5 minutes, with a sample standard deviation of 6.5 minutes. Assuming normality of assembly times, construct a 95% confidence interval estimate for the assembly mean time for this popular toy.

3. A random sample of 550 preschool children revaled that only 319 had been vaccinated and 181 not vaccinated. Construct a 95% confidence interval for the proportion vaccinated.

4. You are the designer for your company's web site. You have data to indicate that the mean download time for the homepage is 5.1 seconds and that the standard deviation of download time is 1.8 seconds. If we assume that the download times are normally distributed, what percent of users will wait between 5 and 10 seconds for the homepage to download?

#### Solution Preview

1.
First, we need to find out the critical t value.
The degree of freedom is 30-1=29.
The critical t value for 95% confidence interval is 2.045 (found in the t table, two tailed P=0.05, degree of freedom is 29)
margin of error=2.045*1150/sqrt(30)=429.4
Upper limit: 27895+429.4=28324.4
Lower limit: 27895-429.4=27465.6
Therefore, the ...

#### Solution Summary

The statistics between 95% confidence intervals. The average amount of time is determined.

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