The lifespans of zebras in a particular zoo are normally distributed. The average zebra lives 20.5years; the standard deviation is 3.9 years. Use the empirical rule (68-95-99.7%)to estimate the probability of a zebra living less than 32.2 years.
Answers
Answer:
Using the empirical rule, the probability of a zebra living less than 32.2 years is about [tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex] or about 99.85%.
Step-by-step explanation:
Roughly speaking, the empirical rule tells us that, in a normal distribution, the distance of one standard deviation from the mean, above and below it, contains approximately 68% of the observations of the normally distributed data; two standard deviations from the mean, above and below it, 95% of the data, and, finally, the distance of three standard deviations from the mean, above and below it, contains 99.7% of the data, approximately.
To estimate probabilities with this rule, we need to use, at least, two concepts: the standard normal distribution and the z-scores. A standard normal distribution is a normal distribution with mean = 0 and standard deviation = 1. It represents standardized data. This standardized data are those coming from a normal distribution and commonly called raw data. The way to standardized them is using the z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
x represents raw data. In this case, x = 32.2 years.
[tex] \\ \mu[/tex] is the population mean. In this case, [tex] \\ \mu = 20.5[/tex] years.
[tex] \\ \sigma[/tex] is the population standard deviation. In this case, [tex] \\ \sigma = 3.9[/tex] years.
Then, using [1], we "transform" the raw score into a z-score (a standardized value) and then use this to find the corresponding probability using the standard normal distribution (or the cumulative standard normal distribution to be more precise), available in any Statistics book or on the Internet.
However, applying the empirical rule, we can estimate those probabilities faster but in an approximate way.
Let us take the corresponding z-score:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{32.2 - 20.5}{3.9}[/tex]
[tex] \\ z = \frac{11.7}{3.9}[/tex]
[tex] \\ z = 3[/tex]
That is, the value z = 3 tells us the raw score 32.2 years is three standard deviations from the mean. In other words, 99.7% of the values are between z = -3 and z = 3. However, we are asked for P(z<3). The remaining area is below z = -3 and above z = 3. Since the normal distribution is symmetrical, we have to divide the remaining area by 2. That is, (1 - 0.997)/2 = 0.003/2 = 0.0015.
The area below z = -3 is, therefore, 0.0015, as well as above z = 3 or P(z<-3) = P(z>3) = 0.0015. The only area that not correspond to P(z<3) is P(z>3). As a result, we need to add the area below z = -3 (0.0015) to the value of 0.997 to finally have P(z<3).
Then
[tex] \\ P(z<3) = P(x<32.2) = 0.997 + P(z<-3)[/tex]
[tex] \\ P(z<3) = P(x<32.2) = 0.997 + 0.0015[/tex]
[tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex]
Thus, using the empirical rule, the probability of a zebra living less than 32.2 years is about [tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex].
In the graph below, we have a representation of the area below z = 3 or P(z<3) = P(x<32.2) is, approximately, 0.9985 or 99.85%.
Notice that using the cumulative standard normal table, as explained before, we have that P(z<3) = 0.99865.
Answer: 68, if the question asks between 16.6 and 24.4 years. 99.85, if the question asks for less.
Step-by-step explanation:
Related Questions
The population of the city of Miami is approximately 463,300 and is increasing at a rate of 3% each year. Use an exponential function to find the population of the city after 7 years. Round to the nearest whole number.
Answers
Step-by-step explanation:
The population of the city of Miami = 463,300
The rate of increase in population every year = 3%
The population of the city after 7 years = ?
By formula, [tex]P_{n} = P (1 +\frac{r}{100})^{n }[/tex]
Pn is the population after 7 years
P is the current population = 463,300
r = 3 %, n = 7
[tex]P_{7} = 463300 (1 +\frac{3}{100})^{7 }[/tex]
= 463300 (1.23)
= 569859
The population of the city after 7 years = 569,859
Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?
Answers
Answer:
D)The height of the red prism is three times the height of the blue prism
Step-by-step explanation:
Here is the complete question
Two rectangular prisms have the same volume. The area of the base of the blue prism is 2 1/6 square units. The area of the base of the red prism is one third that of the blue prism.
which statement is true?
a)The height of the red prism is one-third the height of the blue prism
B)The height of the red prism is the same as the height of the blue prism
C)The height of the red prism is six times the height of the blue prism.
D)The height of the red prism is three times the height of the blue prism
Solution
Since both prisms have the same volume, V = A₁h₁ = A₂h₂ where A₁ and A₂ are the areas of the red and blue prisms respectively and h₁ and h₂ are the heights of the red and blue prisms respectively. For the question, A₁ = A₂/3. Substituting this into the equation, A₁h₁ = A₂h₂
A₂h₁/3 = A₂h₂
h₁ = 3h₂ . So the height of the red prism is thee times the height of the blue prism.
Answer:
D
Step-by-step explanation:
Words to know
Write the letter of the definition next to the matching word as you work through the
lesson. You may use the glossary to help you.
midpoint
A. the point on a graph at which the graph
crosses the x-axis
quadratic function
B. in a parabola, the point at which the
function goes from increasing to
decreasing or vice versa
vertex
C. a point on a line segment that is
equidistant from the two endpoints
x-intercept
D. a second-degree polynomial function that
can be written in the form ax? + bx + c,
where a, b, and c are real constants and a
does not equal zero
Answers
Answer:
Step-by-step explanation:
A. The extreme point which can be the maximum or minimum is called the vertex.
B. Parabolas increase or decrease which refers to the maximum or minimum.
2. The point (0.28, 0.96) lies on the unit circle. Which of the following is closest to the tangent of an angle
drawn in standard position whose terminal ray passes through this point?
(1) 3.43
(2) 1.73
(3) 0.29
(4) 0.42
Answers
Answer:
(1) 3.43
Step-by-step explanation:
tan θ = y / x
tan θ = 0.96 / 0.28
tan θ = 3.43
Option (1) will be the correct option.
Terminal angle:Terminal angle is the angle formed between the initial side and the terminal side (As shown in the figure). Tangent of this angle is the ratio of opposite side and the adjacent side.
[tex]\text{tan}\theta=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
Given in the question,
A point (0.28, 0.96) lies on the unit circle.Terminal angle will be formed between the standard position and the terminal ray passing through the given point.
Hence, [tex]\text{tan}\theta=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(θ) = [tex]\frac{PO}{OA}[/tex]
tan(θ) = [tex]\frac{0.96}{0.28}[/tex]
tan(θ) = 3.43
Therefore, Option (1) will be the correct option.
Learn more about the terminal angle here,
https://brainly.com/question/12561549?referrer=searchResults
I NEED HELP SO BAD I WILL GIVE CROWN
A mechanic had 412 gallons of motor oil at the start of the day. At the end of the day, only 5 pints remained.
How many pints of motor oil did the mechanic use during the day?
4 pt
13 pt
19 pt
31 pt
Answers
Jose completes 2 assignments per day and already completed 5 assignments. He needs to complete a total of 15 assignments. What is the equation matching this scenario?
Answers
Answer: 15 = 2x + 5
Step-by-step explanation:
15 = total
x = days
2 = assignments per day / growth
5 = already done / y-intercept
Please help me with this question
Answers
Answer:
x = 55 degrees.
y = 49 degrees.
Step-by-step explanation:
AB = AD and BC = DC so we have 2 isosceles triangles here thus the base angles are equal.
Therefore m < y = (180 - 82)/2 = 98/2
= 49 degrees.
m < x = (180 - 2*35)/2 = 55 degrees.
Find the slope through the points (2,4) and (6,12)
Answers
Answer:
The slope is 2
Step-by-step explanation:
Slope = [tex]\frac{rise(changeiny)}{run(changeinx)} =\frac{y2-y1}{x2-x1} =\frac{12-4}{6-2} =\frac{8}{4}[/tex]
8/4 reduces to 2/1 which makes the slope 2
The slope of the line is m = 2.
Explanation
To find the slope through two points, you need to apply the following formula:
[tex]\sf m=\cfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values:
[tex]\sf m=\cfrac{12-4}{6-2}[/tex]
[tex]\sf m=\cfrac{8}{4}[/tex]
[tex]\sf m=2[/tex]
Answer: m = 2The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars?
Yes, because the computed t lies in the rejection region.
No, because the information given is not complete.
No, because the computed t lies in the area to the right of -2.718.
Yes, because 43 is greater than 41.5.
Answers
There has been a statistically significant change in the mean length of the candy bars since the computed t value, -2.913, is less than the critical t value of -2.718. Therefore, we reject the null hypothesis that the mean length has not changed.
Explanation:A hypothesis test is performed to test the claim at the 0.02 level that there has been no change in the mean length of candy bars. The null hypothesis is that the mean length remains 43mm, as given. The alternate hypothesis is that the mean length has changed. A sample of twelve bars is taken and with the given data, the computed t value is -2.913.
For a two-tailed test at the 0.02 significance level and degrees of freedom (n-1) equals 11, the critical t values are -2.718 and 2.718. If the computed t value falls beyond this range, that is, below -2.718 or above 2.718, we reject the null hypothesis. In this case, -2.913 is less than -2.718
Therefore, there has been a statistically significant change in the mean length of the bars as the t value lies in the rejection region.
Learn more about Hypothesis Testing here:https://brainly.com/question/31665727
#SPJ3
The correct option is Yes, because the computed t lies in the rejection region. The t-test analysis indicates a statistically significant change in the mean length of candy bars based on the computed t-value falling in the rejection region.
Null Hypothesis (H0): The mean length of the candy bars is 43 mm.
Alternate Hypothesis (Ha): There has been a change in the mean length of the candy bars.
T-Test Analysis: The computed t-value of -2.913 falls in the rejection region, indicating statistical significance, therefore rejecting the null hypothesis. Hence, there has been a statistically significant change in the mean length of the bars.
Solve the problems 11-4 times
Answers
Answer:
12 45 67 88 90
Step-by-step explanation:
if you flip 3 coins what is h the probability you’ll get 2 tail and 1 head in any order?
Answers
Answer:
If you flip three fair coins,what is the probability that you'll get heads on the first two flips and tails on the last flip? So I have 3 coins and I flip them ... If H = Heads and T = Tails, your possible outcomes are. HHH. HHT. HTH. THH. HTT ... So, the probability of HHT is 1/8 = 0.125 = 12.5%. Upvote • 0 Downvote.
Step-by-step explanation:
The ticket price for a one way flight from Orlando to Philadelphia is regularly $149 if malia is purchasing a ticket for the day before thanksgiving and the airline marked the ticket price up 72% find the cost of her ticket
Answers
Answer:
the ticket will cost 256.28
Step-by-step explanation:
you need to multiply the cost of the ticket 149 by .72 and you get 107.28
then add 149 + 107.28 to get 256.28
The dot plot shows how much hairdressers in Margot's area charge for a woman's haircut. The least expensive cut is $25. Margot described the data as having a spread from $25 to $47, seven gaps, a cluster from $35 to $37, and a center of $37. Where did Margot make an error? Price of a Woman's Haircut (in dollars) The spread is from $25 to $46. There are 11 gaps. The cluster is from $36 to $37. The center is at $36
Answers
Answer:
The center of the plot is at $36 rather than $37
Center = $ 36
Step-by-step explanation:
The description by Margot is accurate except for the following observation
From the dot plot there are 31 dots, therefore, the center should be at the median mark of the dot plot of the graph which is the 16th dot.
By looking at the dot plot it is observed that both 16th dot and the middle of the cluster are located on the $37.
That is the point where Margot make an error is defining the center as $37, where the center is observed to be $36.
Answer:
36$
Step-by-step explanation:
Just did it.
Suppose the Marshall Islands have an area of about 70 square miles. Suppose a rectangle, with sides x and 2x + 4, has an area of 70 square miles. Find the value of x?
Answers
Answer:
The value of x is 5.
Step-by-step explanation:
We are given the following in the question:
Area of rectangle = 70 square miles
The sides of the rectangle are:
[tex]w = x, l = (2x+4)[/tex]
Area of rectangle =
[tex]A = l\times w[/tex]
Putting values, we get.
[tex]70 = (2x+4)x\\\Rightarrow 2x^2 + 4x - 70 = 0 \\\Rightarrow 2(x + 7)(x - 5) = 0\\\Rightarrow (x+7) = 0, (x-5) = 0\\\Rightarrow x = -7, x = 5[/tex]
Since, the value of x cannot be negative as it represents side of a rectangle.
Thus, the value of x is 5.
A researcher conducts a related-sample study to evaluate two treatments with n = 16 participants and obtains a t statistic of t = 1.94. The treatment 2 is expected to have a greater sample mean than the treatment 1. What is the correct decision for a hypothesis test using α = .05?
Answers
Answer:
Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim may be supported.
Step-by-step explanation:
Solution:-
- The sample size of two treatments, n = 16
- The mean of sample treatment 1, u1
- The mean of sample treatment 2 , u2
- The significance level, α = .05
- State the hypothesis:
Null hypothesis : u2 - u1 > 0
Alternate hypothesis : u2 - u1 ≤ 0
- The rejection region of the T- critical for lower tailed test.
significance level, α = .05
degree of freedom v = n - 1 = 16 - 1 = 15
T-critical = - 1.75
- The T-test value is compared with T-critical:
T-test = 1.94
T- critical = -1.75
T-test > T-critical .. ( Null not rejected )
- Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim maybe supported.
What is the volume of the cone? 20ft in height 16ft in diameter.
Answers
Answer:
Approximately 1340.41
Step-by-step explanation:
Answer:
[tex]V = 1340.41[/tex]
Step-by-step explanation:
The formula of the cone is [tex]V=\pi r^{2} \frac{h}{3}[/tex]. r = radius (half of diameter) and h = height. Plug in the numbers and solve the equation.
where a and b are the lengths of two of the sides and C is the included angle. If Upper A equals 14 in squared commaa equals 8 in commab equals 7 in commaand C is an acute angle, what must C be? Give your answer in degrees to the nearest hundredth.
Answers
Answer:
[tex]C=40.01^0[/tex]
Step-by-step explanation:
Area =14 Inch squared
a=8 Inch
b = 7 Inch
DEFINITION: An Included Angle is the angle in between two adjacent sides.
Given the lengths of two sides of a triangle and an included angle.
Area of the Triangle, [tex]A=\frac{1}{2}abSinC[/tex]
Substituting the given values:
[tex]A=\frac{1}{2}abSinC\\14=\frac{1}{2}*8*7*SinC\\18=28*Sin C\\Sin C =\frac{18}{28}\\ C=arcsin (\frac{18}{28})=40.01^0[/tex]
Angle C is 40.01 degrees to the nearest hundredth.
Rewrite the following equation in slope-intercept form.
2x – 19y = -4.
Answers
Reduce the equation 5x+7y-35=0 to slope-intercept form, ... Feasible region (shaded) for a LPP is shown in following figure. ... Write the normal form of the equation of the plane 2x-3y+6z+ ... 8^-3x^7y^-11/5x^-19y^17z^-14.
Hope I helped! :)
Iding a go-kart costs $10 on Saturday and Sunday and $5 on Monday through Friday. Is the cost a function of the activity type? Explain why or why not.
Answers
Answer:
Answer is No, ITS NOT.
Refer below.
Step-by-step explanation:
There are two different cost of the same activity i.e. $10 on Saturday and Sunday and $5 on Monday through Friday, So it wouldn't be a function.
A package of Oreos has 36 cookies 89 cookies what is the percentage of the cookies that are left in the package
Answers
Answer:
40.44%
Step-by-step explanation:
I'm assuming you meant to say a package of oreos has 36 cookies out of 89 cookies.
To figure out percentage:
Has #/Out of # = Decimal * 100(add a % at the end)
36/89 = 0.4044 * 100 = 40.44%
Gideon wants to buy a new video game from the store. They are having a sale on all games, and sell the game at a 15% discount. He also has a club card with the store, and gets additional 5% off the sale price. If the original price of the game is $28.00, what is the final sale price that Gideon will pay?
Answers
Answer:
5%+15%=20%
to find 20% of 28 u multiply 28 x 0.2= 5.6
so to remove the 20% since it's 20% off u subtract 5.6 from 28
28-5.6= 22.4
Step-by-step explanation:
Need help fast!!!!!!
Answers
Answer:
There is no answer to this, closest answer is the 1st choice
Step-by-step explanation:
Which is the value of this expression when a = negative 2 and b = negative 3?
(Start Fraction 3 a Superscript negative 3 Baseline b squared Over 2 a Superscript negative 1 Baseline b Superscript 0 Baseline End Fraction) squared
Start Fraction 4 Over 9 End Fraction
Answers
Answer:
iiiiiiiiiiiiiiiiiiiiiiii believe its 8
Step-by-step explanation:
Answer:
729/64
Step-by-step explanation:
:)
How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answers
Answer:
I think it's 5/21.
Step-by-step explanation:
1/3=7/21
3/7=9/21
7/21+9/21=16/21
21/21-16/21=5/21
5/21 can't be reduced.
5/21+7/21+9/21=21/21 or 1
The population of Thomasville was 2,460 in 2006, and is growing at an annual rate of 3.5%. This can be modeled by the exponential function f(x) = 2460(1.035) ^x.
How does the function change over the interval from x=2 to x=3?
A. f(x) increases by 3.5%
B. f(x) decreases by 3.5%
C. f(x) increases by a factor of 2460
D. f(x) decreases by a factor of 2460
Answers
Answer:
A. f(x) increases by 3.5%
Step-by-step explanation:
Given:
City of Thomasville.
Population in 2006, [tex]P_o[/tex] = 2460
Exponential function, f(x) = 2460(1.035) ^x ...equivalent to [tex]P=P_o(1+r)^t[/tex]
Function change at x = 2, 3
According to the question:
Plugging the values of x= 2 and x=3 we have to find the population at different x.
So,
At x= 2 At x=3
⇒ [tex]P_2=P_o(1+r)^t[/tex] ⇒ [tex]P_3=P_o(1+r)^t[/tex]
⇒ [tex]P_2=2460(1.035)^x[/tex] ⇒ [tex]P_3=2460(1.035)^x[/tex]
⇒ [tex]P_2=2460(1.035)^2[/tex] ⇒ [tex]P_3=2460(1.035)^3[/tex]
⇒ [tex]P_2=2622.4[/tex] ⇒ [tex]P_3=2707.7[/tex]
Percent change :
⇒ [tex]\triangle \% =\frac{Final\ value -Initial\ value}{Initial\ value} \times 100[/tex]
⇒ [tex]\triangle \% = \frac{(P_3-P_2)}{P_2} \times 100[/tex]
⇒ [tex]\triangle \% = \frac{(2707.7-2622.4)}{2622.4} \times 100[/tex]
⇒ [tex]\triangle \% = 3.5[/tex]
So,
The function f(x) increases by 3.5% option A is the right choice.
Suppose your parents started saving for your college education when you were 5 years old. Assume they saved $300 the first year, $325 the second year, $350 the third year, and so on increasing each year contribution by $25 if you are 17 in the last year of contribution how much will have been saved in all ?
Answers
Answer:
$575
Step-by-step explanation:
the explanation is in the picture
please like and Mark as brainliest
Vince worked 675 hours in 15 weeks. At what rate did he work in hours per week?
Answers
Answer:
45 hours a week
Step-by-step explanation:
Ok, so we know that he worked 675 hours in 15 weeks.
So all we need to do is divide the hours by the amount of weeks, which is 15:
675/15= 45
So he worked 45 hours a week!
what is the ratio of the areas between a 16” pizza and a 12” pizza
Answers
Step-by-step explanation:
Ratio of pizza =
16 : 12 = 8 : 6 = 4 : 3
Which of the following is correct about a probability distribution? Select one: a. The sum of all probabilities of possible outcomes must equal 1.0. b. The outcomes must be mutually exclusive. c. The probability of each outcome must be between 0.0 and 1.0 inclusive d. All of these answers are correct
Answers
Answer: All of the answers are correct.
Step-by-step explanation:
A probability distribution is the collection of probabilities which defines the likelihood of observing all the various outcomes of an experiment or event. A probability distribution has two main properties which are that:
• Each probability in the distribution consist of a value between 0 and 1.
• The sum of all probabilities in the distribution equals 1.
Also, in probability, an outcome is the possible result of an experiment and each possible outcome gotten is unique, therefore the different outcomes are mutually exclusive i.e. only one outcome can occur on each trial during the experiment.
The sum of all probabilities of possible outcomes in a probability distribution must equal 1.0, and the probability of each outcome must be between 0.0 and 1.0, inclusive.
A probability distribution is a function that assigns probabilities to all possible outcomes of an experiment. The correct statement about a probability distribution is that the sum of all probabilities of possible outcomes must equal 1.0. This is known as the axiom of probability. In addition, the probabilities of each outcome must be between 0.0 and 1.0, inclusive. This ensures that probabilities are valid and within the appropriate range. The outcomes themselves do not have to be mutually exclusive; they can overlap or have common elements.
Learn more about probability here:https://brainly.com/question/32117953
#SPJ3
Tom gets $12 off a box of chocolates that had an original price of $48.What percentage is the discount
Answers
Answer:
25 percent
Step-by-step explanation:multiply 48 by .25 it will give you 12 which is the discount hope this helps god bless
Answer:
25%
Step-by-step explanation:
12/48=.25=25%