Question

1. Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6-in and a standard deviation of 1.2-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.9% or largest 1.9%.

a) What is the minimum head breadth that will fit the clientele?

            min =

b) What is the maximum head breadth that will fit the clientele?

      min =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

2) You measure 48 dogs' weights, and find they have a mean weight of 54 ounces. Assume the population standard deviation is 12.9 ounces. Based on this, construct a 90% confidence interval for the true population mean dog weight.

Give your answers as decimals, to two places

_______ ± _______ ounces

3) Assume that a sample is used to estimate a population mean μ. Find the margin of error M.E. that corresponds to a sample of size 23 with a mean of 66.3 and a standard deviation of 19.9 at a confidence level of 99%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.

M.E. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

4) The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 40.2 for a sample of size 305 and standard deviation 6.9.

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level).

Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

_____ < μ < ______

Answer should be obtained without any preliminary rounding.

Answer 1

1)

Given information,

we know that,

to find the head breadths that are in the smallest 1.9% or largest 1.9%,

the z value correponding to 0.019 from the standard z table is,

Therefore,

Minimum head breadth that will fit the clientele is,

Min = 6+(-2.075*1.2)

= 3.5 in

Maximum head breadth that will fit the clientele is,

Max = 6+(2.075*1.2)

= 8.5 in

2)

The given information is,

mean weight,

population standard deviation,

Number of samples, n = 48

z value corresponding to 90% confidence level = 1.6449

we know that,

3)

Given information,

sample of size, n = 23

mean of,

standard deviation,

confidence level = 99%

Z value corresponding to 99% confidence level is 2.58

4.

Given information,

Average reduction in systolic blood pressure,

sample size,n = 305

standard deviation, s = 6.9

z value corresponding to 90% confidence level = 1.6449