Mathematics: A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 13.6 reproductions and the population standard deviation is known to be 1.9. If a sample of 189 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.

32.07Step-by-step explanation:12.88+44.95=32.07...

A research scientist wants to know how many times

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31.01.2022

The confidence interval is $13.4< \mu < 13.8$

Step-by-step explanation:

From the question we are told that

The sample mean is $\= x = 13.6$

The standard deviation is $\sigma = 1.9$

The sample size is n = 189

given that the confidence level is 85% then the level of significance is mathematically represented as

$\alpha = (100 - 85 )\%$

$\alpha = 0.15$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{\alpha }{2} } = 1.44$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.44* \frac{1.9}{\sqrt{189} }$

=> E = 0.1990

The 85% confidence interval is mathematically represented as

$\= x - E < \mu$

=> $13.6- 0.1990 < \mu < 13.6+ 0.1990$

=> $13.4< \mu < 13.8$

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