91Ó°ÊÓ

Consider a normal distribution with mean \(\mu=2354\) points and standard deviation \(\sigma=468\) points. (a) Find the third quartile \(Q_{3}\) of the distribution rounded to the nearest point. (b) Find the first quartile \(Q_{1}\) of the distribution rounded to the nearest point.

A normal distribution has standard deviation \(\sigma=12.3\) points and the 84 th percentile of the distribution is \(P_{84}=66.7\) points. (a) Find the median \(\mu\). (b) Find the 16 th percentile \(P_{16}\).

A normal distribution has standard deviation \(\sigma=6.1 \mathrm{~cm},\) and the 97.5 th percentile of the distribution is \(P_{97.5}=81.5 \mathrm{~cm}\). Find the mean \(\mu\).

A normal distribution has mean \(\mu=12.6\) and standard deviation \(\sigma=4.0 .\) Approximately what percent of the data fall between 9.9 and \(16.6 ?\)

A normal distribution has mean \(\mu=500\) and standard deviation \(\sigma=35 .\) Approximately what percent of the data fall between 465 and \(605 ?\)

In a normal distribution, what percent of the data have \(z\) -values satisfying (a) \(z \leq 2\) ? (b) \(1 \leq z \leq 2 ?\)

A dishonest coin with probability of heads \(p=0.75\) is tossed \(n=1200\) times. Let the random variable \(X\) represent the number of times the coin comes up heads. (a) Find the mean and standard deviation for the distribution of \(X\). (b) Find the first and third quartiles for the distribution of \(X\). (c) Find the probability that the number of heads will fall somewhere between 900 and \(945 .\)

Find the \(z\) -value of (a) the first quartile of a normal distribution. (b) the third quartile of a normal distribution.

The distribution of weights for six-month-old baby boys has mean \(\mu=8.16 \mathrm{~kg}\) and standard deviation \(\sigma=0.95 \mathrm{~kg}\) (see Exercise 53 ). (a) Suppose that a six-month-old baby boy weighs in the 95th percentile of his age group. Estimate his weight in kilograms rounded to two decimal places. (b) Suppose that a six-month-old baby boy weighs in the 20th percentile of his age group. Estimate his weight in kilograms rounded to two decimal places.

Explain why when the dishonest-coin principle is applied to an honest coin \((p=1 / 2),\) we get the honest-coin principle.