Given that a 90% confidence interval for the mean height of all adult males in Idaho measured in inches was [62.532, 76.478]. Use this to answer all parts. Part 1: What was the point estimate used to estimate the mean height of all adult males in Idaho?

The confidence interval on this case is given by:

(1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

So then the mean for this case is 69.505

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

represent the sample mean  

population mean (variable of interest)  

represent the population standard deviation  

n represent the sample size  

Assuming the X follows a normal distribution  

The confidence interval on this case is given by:

(1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

So then the mean for this case is 69.505

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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