Question The accompanying table shows the number of bacteria present in a certain culture over a 6 hour period, where x is the time, in hours, and y is the number of bacteria. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the number of bacteria present after 11 hours, to the nearest whole number.

Hours(x) Bacteria (y)

0 1391

1 1560

2 1689

3 2013

4 2160

5 2504

6 2744

In a certain orchard, the number of apples (a) in a tree is normally distributed with a mean of 300 apples and a standard deviation of 30 apples. Find the. probability that a given tree has between 240 and 330 apples.

Be sure to use the\( 68 \% - 95 \% - 99.7 \% \)rule and do not round.

Determine if the finite correction factor should be used. If so, use it in your calculations when you find the probability.

In a sample of 800 gas stations, the mean price for regular gasoline at the pump was $2.813 per gallon and the standard deviation was $0.008 per gallon. A random sample of size 50 is drawn from this population. What is the probability that the mean price per gallon is less than $2.812 ?

The probability that the mean price per gallon is less than $2.812 is

(Round to four decimal places as needed.)

In a random sample of 8 people, the mean commute time to work was 33.5 minutes and the standard deviation was 7.4 minutes. A 98% confidence interval using the t-distribution was calculated to be ( 25.7,41.3 ). After researching commute times to work, it was found that the population standard deviation is 8.7 minutes. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

The margin of error of\(\mu \)is\(\square \)

(Round to two decimal places as needed.)

Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean and\( \sigma = 12.8 \). Assume the population is normally distributed.

A 95% confidence level requires a sample size of\( \square \).

(Round up to the nearest whole number as needed.)