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
Elina [12.6K]
3 years ago
11

An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 90 and a stan

dard deviation of 12. Use StatCrunch to find the proportion of children have an index of at least 110.
Mathematics
1 answer:
weqwewe [10]3 years ago
8 0

Answer:

The proportion of children that have an index of at least 110 is 0.0478.

Step-by-step explanation:

The given distribution has a mean of 90 and a standard deviation of 12.

Therefore mean, \mu = 90 and standard deviation, \sigma = 12.

It is given to find the proportion of children having an index of at least 110.

We can take the variable to be analysed to be x = 110.

Therefore we have to find p(x < 110), which is left tailed.

Using the formula for z which is p( Z < \frac{x - \mu}{\sigma}) we get p(Z < \frac{110 - 90}{12} = 1.67).

So we have to find p(Z ≥ 1.67) = 1 - p(Z < 1.67)

Using the Z - table we can calculate p(Z < 1.67)  = 0.9522.

Therefore p(Z ≥ 1.67) = 1 - 0.9522 = 0.0478

Therefore the proportion of children that have an index of at least 110 is 0.0478

You might be interested in
This claim is to be investigated at .01 levels. “Forty percent or more of those persons who retired from an industrial job befor
Degger [83]

According to the described situation, we have that:

  • The null hypothesis is H_0: p < 0.4

The decision rule is:

  • z < 2.327: Do not reject the null hypothesis.
  • z > 2.327: Reject the null hypothesis.

The value of the test statistic is of z = -0.866.

<h3>What is the null hypothesis?</h3>

The claim is:

"Forty percent or more of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available"

At the null hypothesis, we consider that the claim is false, that is, the proportion is of less than 40%, hence:

H_0: p < 0.4

<h3>What is the decision rule?</h3>

We have a right-tailed test, as we are testing if a proportion is less/greater than a value. Since we are working with a proportion, the z-distribution is used.

Using a z-distribution calculator, the critical value for a right-tailed test with a significance level of 0.01 is of z = 2.327, hence, the decision rule is:

  • z < 2.327: Do not reject the null hypothesis.
  • z > 2.327: Reject the null hypothesis.

<h3>What is the test statistic?</h3>

The test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

In which:

  • \overline{p} is the sample proportion.
  • p is the proportion tested at the null hypothesis.
  • n is the sample size.

In this problem, the parameters are:

p = 0.4, n = 200, \overline{p} = \frac{74}{200} = 0.37

Hence:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

z = \frac{0.37 - 0.4}{\sqrt{\frac{0.4(0.6)}{200}}}

z = -0.866

The value of the test statistic is of z = -0.866.

You can learn more about hypothesis tests at brainly.com/question/16313918

7 0
2 years ago
Find the area of this shape
Lilit [14]

9 \times 13 = 117 {cm}^{2}
4 0
3 years ago
Drag steps into order to correctly solve the equation 4x = 112 for x.
alekssr [168]
4x=112
x=112/4      ( '/' means divide)
x=28
5 0
3 years ago
Read 2 more answers
The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu
rjkz [21]

The balloon has a volume V dependent on its radius r:

V(r)=\dfrac43\pi r^3

Differentiating with respect to time t gives

\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}

The surface area of the balloon is

S(r)=4\pi r^2

and differentiating gives

\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}

so that at the moment the radius is 3 m, its area is increasing at a rate of

\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}

4 0
3 years ago
Given the function below, find f(7) f(x)=-x^2+9x
sashaice [31]

Answer:

14

f(x) = 7

-7^2 + 9(7)= -49 + 63 = 14

3 0
3 years ago
Other questions:
  • May someone explain please?
    12·1 answer
  • Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b obtuse. What must be true?​
    15·2 answers
  • Answer questions below<br> ASAP<br> 5-1/2x=5/8x+2
    14·1 answer
  • The elk population in an area is increasing. This year, the population was 1.076 times last year's population of 1537.
    12·1 answer
  • Can someone help? anyone who's taking like geometry?
    8·1 answer
  • What is the number 4,305,012 written in expanded form
    5·1 answer
  • HELP AGANI PLZ
    13·1 answer
  • Please help me please please help please
    15·1 answer
  • In Mrs. Wison's math dass, the ratio of girls
    6·1 answer
  • There are 12 girls and 16 boys . What is the largest number in each group?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!