In a certain distribution of numbers, the mean is 100 with a standard deviation of 7. At least what fraction of the numbers are between 37 and 163



Answer to a math question In a certain distribution of numbers, the mean is 100 with a standard deviation of 7. At least what fraction of the numbers are between 37 and 163

Expert avatar
62 Answers
To find the fraction of numbers between 37 and 163, we need to first find the z-scores for these values and then use the z-table to find the corresponding probabilities.

The z-score formula is given by:
z = \frac{x - \mu}{\sigma}
- x is the value
- \mu = 100 is the mean
- \sigma = 7 is the standard deviation

For x = 37 :
z_{37} = \frac{37 - 100}{7} = -9

For x = 163 :
z_{163} = \frac{163 - 100}{7} = 9

Next, we look up the z-scores -9 and 9 in the z-table. We find that for a z-score of -9, the probability is close to 0, and for a z-score of 9, the probability is close to 1.

Therefore, the fraction of numbers between 37 and 163 is close to 1 (or 100%).

\textbf{Answer:} \frac{100}{100} = 1

Frequently asked questions (FAQs)
Find the value of sine (π/4) - cosine (π/6).
What is the vertex.form of a parabola function with an equation 𝑦 = 2𝑥² + 4𝑥 - 3?
Math Question: Factor the expression 6x² + 5x - 6 using the distributive property. What are the resulting factors?
New questions in Mathematics
a runner wants to build endurance by running 9 mph for 20 min. How far will the runner travel in that time period?
5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] ÷ (2/-5)} . 8/15
11(4x-9)= -319
Solve: −3(−2x+23)+12=6(−4x+9)+9.
Kayla has $8,836.00 in her savings account. The bank gives Kayla 5%of the amount of money in account as a customer bonus. What amount of money does the bank give Kayla? Justify your answer on a 6th grade level.
How many kilometers does a person travel in 45 minutes if they move at a rate of 8.3 m/s?
Find the measures of the sides of ∆KPL and classify each triangle by its sides k (-2,-6), p (-4,0), l (3,-1)
Moaz wanted to test whether the level of headache pain (on a scale of 1 – 10) changes after taking Advil. He collected data from 9 participants and calculated the difference in headache pain before and after taking Advil (summarized in the table below). Determine W observed for this test. Difference Scores -2 -4 0 +1 +3 -2 0 -3 -5 Also, What is the degrees of freedom for this test?
Divide 22 by 5 solve it by array and an area model
Estimate the fifth term if the first term is 8 and the common ratio is -1/2
How many different ways can a psychology student select 5 subjects from a pool of 20 subjects and assign each one to a different experiment?
We have spent 1/4 of the inheritance on taxes and 3/5 of the rest on buying a house. If the inheritance was a total of €150,000 How much money do we have left?
3. A rock is dropped from a height of 16 ft. It is determined that its height (in feet) above ground t seconds later (for 0≤t≤3) is given by s(t)=-2t2 + 16. Find the average velocity of the rock over [0.2,0.21] time interval.
With the aim of identifying the presence of the feline leukemia virus (FeLV), blood samples were collected from cats sent to a private veterinary clinic in the city of Belo Horizonte. Among the animals treated, it was possible to observe that age followed a Normal distribution with a mean of 4.44 years and a standard deviation of 1.09 years. Considering this information, determine the value of the third quartile of the ages of the animals treated at this veterinary clinic. ATTENTION: Provide the answer to exactly FOUR decimal places
User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v(t). A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.
Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two) au=a.(x,y)=(ax+a-1,ay-2a+2) It is known that this set with the operations defined above is a vector space. A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2 B) show that (0,0) #0 Suggestion find a vector W such that u+w=u C) who is the vector -u D) show that axiom A4 holds:-u+u=0
How to factorise 5y^2 -7y -52
nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities. 65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north
if y=1/w^2 yw=2-x; find dy/dx