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Chapter 6: Q2 (page 240)

Normal Distribution A normal distribution is informally described as a probability distribution that is 鈥渂ell-shaped鈥� when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.

Short Answer

Expert verified

The rough sketch of the normal curve is shown below.

Step by step solution

01

Given information

A normal distribution is bell-shaped.

02

Define a normal distribution

A normal distribution shows a bell shape where the curve rises from left to right, reaching the height at the mean value and then decreasing symmetrically.

03

Step 3:Sketch the normal curve

The sketch of a normal curve is shown below.

The graph is sketched on two axes; the values of a random variable and the corresponding values of the random variables of normal distribution and the probabilities.

The graph is sketched below.

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Most popular questions from this chapter

In Exercises 11鈥�14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in鈥侰oca-Cola鈥俍ero,鈥侱iet鈥侾epsi,鈥侱r鈥侾epper,鈥俛nd鈥侻ellow鈥俌ello鈥俍ero.

Assume鈥倀hat鈥� random samples of size n = 2 are selected with replacement.

Sampling Distribution of the Variance Repeat Exercise 11 using variances instead of means.

In Exercises 11鈥�14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in鈥侰oca-Cola鈥俍ero,鈥侱iet鈥侾epsi,鈥侱r鈥侾epper,鈥俛nd鈥侻ellow鈥俌ello鈥俍ero.

Assume鈥倀hat鈥� random samples of size n = 2 are selected with replacement.

Sampling Distribution of the Median Repeat Exercise 11 using medians instead of means.

Redesign of Ejection SeatsWhen women were finally allowed to become pilotsoffighter jets, engineers needed to redesign the ejection seats because they had been originallydesigned for men only. The ACES-II ejection seats were designed for men weighing between

140 lb and 211 lb. Weights of women are now normally distributed with a mean of 171 lb and astandard deviation of 46 lb (based on Data Set 1 鈥淏ody Data鈥滱ppendix B).

a.If 1 woman is randomly selected, find the probability that her weight is between 140 lb and 211 lb.

b.If 25 different women are randomly selected, find the probability that their mean weight is between 140 lb and 211 lb.

c.When redesigning the fighter jet ejection seats to better accommodate women, which probability is more relevant: the result from part (a) or the result from part (b)? Why?

In Exercises 9鈥�12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Durations of PregnanciesThe lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

a. In a letter to 鈥淒ear Abby,鈥� a wife claimed to have given birth 308 days after a brief visit fromher husband, who was working in another country. Find the probability of a pregnancy lasting308 days or longer. What does the result suggest?

b. If we stipulate that a baby is prematureif the duration of pregnancy is in the lowest 3%,find the duration that separates premature babies from those who are not premature. Premature babies often require special care, and this result could be helpful to hospital administrators in planning for that care.
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