Question

A psychologist finds that the intelligence quotients of a group of patients are normally distributed, with a mean of 104 and a standard deviation of 16. Find the percent of the patients with the following IQs.

(a) above 116

%

(b) between 92 and 122

Answer #1

Solution :

Given that ,

mean = = 104

standard deviation = = 16

(a)

P(x > 116) = 1 - P(x < 116)

= 1 - P[(x - ) / < (116 - 104) / 16)

= 1 - P(z < 0.75)

= 1 - 0.7734

= 0.2266

Percent = **22.66%**

(b)

P(92 < x < 122) = P[(92 - 104)/ 16) < (x - ) / < (122 - 104) / 16) ]

= P(-0.75 < z < 1.125)

= P(z < 1.125) - P(z < -0.75)

= 0.8697 - 0.2266

= 0.6431

Percent = **64.31%**

Use the z-score table to answer the question. Note:
Round z-scores to the nearest hundredth and then find the
required A values using the table.
A psychologist finds that the intelligence quotients of a group of
patients are normally distributed, with a mean of 99 and a standard
deviation of 16. Find the percent of the patients with the
following IQs.
(a) above 111
(b) between 87 and 117

Intelligence quotients (IQs) are normally distributed with a
mean of 100 and standard deviation of 15. Use the 68-95-99.7 Rule
to determine the percentage of people with IQ below 70.
Group of answer choices
a. 95%
b. 2.5%
c. 68%
d. 5%

A.) Suppose a population is known to be normally distributed
with a mean, μ, equal to 116 and a standard deviation, σ, equal to
14. Approximately what percent of the population would be between
116 and 144?
B.) Suppose a population is known to be normally distributed
with a mean, μ, equal to 116 and a standard deviation, σ, equal to
14. Approximately what percent of the population would be between
116 and 130?
C.) Suppose a population is known...

The intelligence quotient (IQ) score, as measured by the
Stanford-Binet IQ test, is normally distributed in a certain
population of children. The mean IQ score is 96 points, and the
standard deviation is 15.72 points. Convert the following into
z-scores:
a) x = 117
b) x = 132
c) x = 92
c) x = 72

1. Suppose a population is known to be normally distributed with
a mean, μ, equal to 116 and a standard deviation, σ, equal to 14.
Approximately what percent of the population would be between 102
and 144?
2. Suppose a population is known to be normally distributed with
a mean, μ, equal to 116 and a standard deviation, σ, equal to 14.
Approximately what percent of the population would be between 102
and 130?
3. Suppose a population is known...

IQs are known to be normally distributed with mean 100 and
standard deviation 15. In a random sample of 37 people, find the
probability that the average IQ is between 96 and 103.

The distribution of weights of a large group of high school
students is normally distributed with mean 55 kg and standard
deviation 5 kg. Which of the following is true?a. About 16 percent
of the students will be over 60 kg. b. About 2.5 percent will be
below 45 kg. c. Half of them can be expected to weigh less than 55
kg. d. About 5 percent will weigh more than 63 kg. e. All the above
are true.

An educational psychologist at a large university wants to
estimate the mean IQ of the students in tertiary institutes in
Macau. A random sample of 15 students (in universities in Macau)
gives the following data on IQs. From further investigation, the
data are normally distributed.
113
120
103
118
104
98
110
126
88
110
126
112
120
101
115
a. At the 5% significance level, do the data
provide sufficient evidence to conclude that the IQ of tertiary
students...

The cholesterol levels of a group of young women at a university
are normally distributed, with a mean of 180 and a standard
deviation of 38. What percent of the young women have the following
cholesterol levels? (Round your answers to one decimal place.)
(a) greater than 217
(b) between 183 and 220

A.) A certain intelligence test has scores that are normally
distributed with a mean of 100 and a standard deviation of 10. An
individual takes the test and converts his score to a Z-score which
he calculates to be 1.5. This corresponds to an actual test score
of?
B.) Boiling point measurements for a liquid under fluctuating
pressure conditions is normally distributed with
mean 98 degrees and standard deviation 0.5. The probability that
a boiling point measurement exceeds 99 degrees...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 43 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago