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Chapter 4: Q84E (page 262)

Find the area under the standard normal probability distribution between the following pairs of z-scores:

a)z=0andz=2.00

b)z=0andz=3

c)z=0andz=1.5

d)z=0andz=.80


Short Answer

Expert verified

A probability distribution is a statistical distribution that specifies all potential values as well as potential outcomes for a random variable within a particular range. The likelihood of an event happening. A probability distribution is a table as well as a formula that associates every result of a statistical study with its occurrence probability.

Step by step solution

01

(a) The data is given below

The calculation is given below:

z=0andz=2

To find the area between 0 and 2 are:


P(0<z<2)=0.4772

The chart is given below:

02

(b) The data is given below

The calculation is given below:


z=0andz=3

To find the area between 0 and 3 are:

P(0<z<3)=0.4987

The chart is given below:

03

(c) The data is given below

The calculation is given below:


z=0andz=1.5

To find the area between 0 and 1.5 are:

P(0<z<1.5)=0.4332

The chart is given below:

04

(d) The data is given below

The calculation is given below:

z=0andz=0.80

To find the area between 0 and 0.80 are:

P(0<z<0.80)=0.2881

The chart is given below:

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Most popular questions from this chapter

Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of the power quality of a transformer, Exercise 2.127 (p. 132). Recall that two causes of poor power quality are 鈥渟ags鈥� and 鈥渟wells.鈥�. (A sag is an unusual dip, and a swell is an unusual increase in the voltage level of a transformer.) For Turkish transformers built for heavy industry, the mean number of sags per week was 353, and the mean number of swells per week was 184. As in Exercise 2.127, assume the standard deviation of the sag distribution is 30 sags per week, and the standard deviation of the swell distribution is 25 swells per week. Also, assume that the number of sags and number of swells is both normally distributed. Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week.

a. What is the probability that the number of sags per week is less than 400?

b. What is the probability that the number of swells per week is greater than 100?

If x is a binomial random variable, compute for each of the following cases:

  1. n = 4, x = 2, p = .2
  2. n = 3, x = 0, p = .7
  3. n = 5, x = 3, p = .1
  4. n = 3, x = 1, p = .9
  5. n = 3, x = 1, p = .3
  6. n = 4, x = 2, p = .6

Blood diamonds. According to Global Research News (March 4, 2014), one-fourth of all rough diamonds produced in the world are blood diamonds, i.e., diamonds mined to finance war or an insurgency. (See Exercise 3.81, p. 200.) In a random sample of 700 rough diamonds purchased by a diamond buyer, let x be the number that are blood diamonds.

a. Find the mean of x.

b. Find the standard deviation of x.

c. Find the z-score for the value x = 200.

d. Find the approximate probability that the number of the 700 rough diamonds that are blood diamonds is less than or equal to 200.

Give the z-score for a measurement from a normal distribution for the following:

a. 1 standard deviation above the mean

b. 1 standard deviation below the mean

c. Equal to the mean

d. 2.5 standard deviations below the mean

e. 3 standard deviations above the mean

Suppose x is a normally distributed random variable with 渭= 11 and 蟽= 2. Find each of the following:

a)P(10鈮�蠂鈮�12)

b) P(6鈮�蠂鈮�10)

c)P(13鈮�蠂鈮�16)

d)P(7.8鈮�蠂鈮�12.6)

e)P(蠂鈮�13.24)

f)P(蠂鈮�7.62)
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