Statistics and Probability Answers

A random sample of 170 boys from 8502 boys in an area showed
that 21 had some nutritional deficiency. Estimate the proportion
of nutritionally deficient boys and the standard error of your
estimate. Give the confidence interval also.

Most people think that the “normal” adult body temperature is 98.6 degrees. That figure based on 19th- century study, has recently been challenged. In a 1992 article in the journal of the American medical association, researchers reported that a more accurate figure may be 98.2 degree. Furthermore the standard deviation appeared to be around 0.7 degrees. Assume that a normal model is appropriate.
a) in what interval would you expect most people’s body temps to be? Explain
b) what fraction of people would be expected to have body temperatures above 98.6?
c) Below what body temp are the coolest 20% of all people?

A tire manufacturer believes that the tread life of its snow tires can be described by a normal model with a mean of 32,000 miles and a standard deviation of 2500 miles.
a) if you buy one of these tires, would it be reasonable for you to hope it will last 40,000 miles? explain
b) approx. what fraction of these tires can be expected to last less than 30,000 miles?
c) approx. what fraction of these tires can be expected to last between 30,000 and 35,000 miles?

Count: 100
Mean: 83.59
Median:93
Standard deviation: 22.26
IQR:17
Q1:80
Q3:97
a) Which is better summary of the percentage of white residents in the neighborhood, the mean or median.
b) Which is a better summary of the spread, the IQR or the standard deviation? Explain.

Based on the Normal model N(100,16) describing IQ scores, what percent of people's IQs would you expect to be:
a) over 80%
b) under 90%
c) between 112 and 132

A random sample of 10 males from a normal population showed a mean height 66
inches and the sum of squares from this mean is equal to 90 sq inches. Is it
reasonable to believe that the average height is greater than 64 inches. Justify your
answer.

Out of 25 newborn babies of obese women, 10 weigh less than 2.5 kg. Find a 95%
confidence interval for the probability that the weight of a newborn baby of an
obese woman is less than 2.5 kg.

A normal population has a mean of 0.1 and standard deviation 2.1. Find the
probability that the mean of a sample of size 900 will be negative.

A random sample of size 64 has been drawn from a population with standard
deviation 20. The mean of the sample is 80.
i) Calculate 95% confidence limits for the population mean
ii) How does the width of the confidence interval changes if the sample size is
256 instead?

The mean and the standard deviation of 20 items is found to be 10 and 2
respectively. At the time of checking it was found that one items with value 8 was
incorrect. Calculate the mean and standard deviation if the wrong item is omitted.