1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
yan [13]
3 years ago
11

. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 5, what is the probability that a person

selected at random will have an IQ of 110 or greater?
Mathematics
1 answer:
bulgar [2K]3 years ago
5 0

Answer:

2.28% probability that a person selected at random will have an IQ of 110 or greater

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 100, \sigma = 5

What is the probability that a person selected at random will have an IQ of 110 or greater?

This is 1 subtracted by the pvalue of Z when X = 110. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{110 - 100}{5}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that a person selected at random will have an IQ of 110 or greater

You might be interested in
You believe the population is normally distributed. Find the 80% confidence interval. Enter your answer as an open-interval (i.e
victus00 [196]

You intend to estimate a population mean μ from the following sample. 26.2 27.7 8.6 3.8 11.6 You believe the population is normally distributed. Find the 80% confidence interval.  Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places.

Answer:

The  Confidence interval = (8.98 , 22.18)

Step-by-step explanation:

From the given information:

mean = \dfrac{ 26.2+ 27.7+ 8.6+ 3.8 +11.6 }{5}

mean = 15.58

the standard deviation \sigma = \sqrt{\dfrac{\sum(x_i - \mu)^2 }{n}}

the standard deviation = \sqrt{\dfrac{(26.2  - 15.58)^2 +(27.7 - 15.58)^2 +(8.6  - 15.58)^2 + (3.8  - 15.58)^2  + (11.6  - 15.58)^2  }{5 }  }

standard deviation = 9.62297

Degrees of freedom df = n-1

Degrees of freedom df = 5 - 1

Degrees of freedom df = 4

For df  at 4 and 80% confidence level, the critical value t from t table  = 1.533

The Margin of Error M.O.E = t \times \dfrac{\sigma}{\sqrt{n}}

The Margin of Error M.O.E = 1.533 \times \dfrac{9.62297}{\sqrt{5}}

The Margin of Error M.O.E = 1.533 \times 4.3035

The Margin of Error M.O.E = 6.60

The  Confidence interval = ( \mu  \pm M.O.E )

The  Confidence interval = ( \mu  +  M.O.E , \mu - M.O.E )

The  Confidence interval = ( 15.58 - 6.60 , 15.58 + 6.60)

The  Confidence interval = (8.98 , 22.18)

7 0
3 years ago
Give a description of a 3/4 turn of the minute hand on a clock face
Snowcat [4.5K]
3/4 on the minute hand of a clock would be 45.

example: 6:45
8 0
3 years ago
PLEASE HELP ME !! ILL MARK U BRAINIEST
madreJ [45]

Answer:

<h2>My name: CORN CORNELIUS CORNWALL</h2><h2>My Age: 209374329 years old</h2><h2>Fav song : Baby by justin bieber</h2><h2>most legendary thing My name: CORN CORNELIUS CORNWALL</h2><h2>My Age: 209374329 years old</h2><h2>Fav song : Baby by justin bieber</h2><h2>most legendary thing that i got : clbsdbdbfdbub penguin membershipMy name: CORN CORNELIUS CORNWALL</h2><h2>My Age: 209374329 years old</h2><h2>Fav song : Baby by justin bieber</h2><h2>most legendary thing that i got : club penguin membershipthat i got : club penguin membership</h2>

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Find the missing exponent in each expression
Naily [24]

Answer:

See below.

Step-by-step explanation:

Multiplying terms with exponents make the exponents add together.

13.) x² · x⁵ = x⁷

14.) b⁵ ·  b³ = b⁸

15.) y⁴ · y⁷ = y¹¹

16.) m⁴ · m¹ = m⁵

8 0
3 years ago
A computer manufacturer releases a new laptop model. The total sales of this computer can be modeled by the function S(t)=75/1+5
maksim [4K]
The answer is 23445.90
4 0
3 years ago
Read 2 more answers
Other questions:
  • the pattern below follows the rule "starting with a value of 3, every consecutive row has a value that is 2 less than twice the
    13·1 answer
  • Nathan estimate 67×36 by finding 70×40. will nathan's estimate be greater than or less than the actual product?explain
    10·2 answers
  • Ten times the sum of half of a number and 6 is 8
    5·1 answer
  • A pyramid with a square base that is 10 cm on a side has a height of 12 cm. The volume of the pyramid is cm3.a0
    11·1 answer
  • Some farmers use a circular irrigation method. An irrigation arm acts as the radius of an irrigation circle. How much land is co
    8·1 answer
  • Convert 5.86 to a percent. A. 586% B. 58.6% C. 5.86% D. 0.0586%
    11·1 answer
  • Find x and y in to the diagram​
    9·1 answer
  • Find the exact value of sin 30° in simplest form with a rational denominator.
    12·1 answer
  • the total number of matches in 8 boxes was 384 how many matches could be there in 35 similar marches boxes​
    8·1 answer
  • Slope = 1/2, through: (3, 1)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!