Harper deposited $110 into a savings account that earns 3.5% interest a year. The function (R)t models the amount of money Raymo
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Answer:
(a) Probability that a single randomly selected element X of the population is between 57,000 and 58,000 = 0.46411
(b) Probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = 0.99621
Step-by-step explanation:
We are given that a normally distributed population has mean 57,800 and standard deviation 75, i.e.; = 57,800 and
= 750.
Let X = randomly selected element of the population
The z probability is given by;
Z = ~ N(0,1)
(a) So, P(57,000 <= X <= 58,000) = P(X <= 58,000) - P(X < 57,000)
P(X <= 58,000) = P( <=
) = P(Z <= 0.27) = 0.60642
P(X < 57000) = P( <
) = P(Z < -1.07) = 1 - P(Z <= 1.07)
= 1 - 0.85769 = 0.14231
Therefore, P(31 < X < 40) = 0.60642 - 0.14231 = 0.46411 .
(b) Now, we are given sample of size, n = 100
So, Mean of X, X bar = 57,800 same as before
But standard deviation of X, s = =
= 75
The z probability is given by;
Z = ~ N(0,1)
Now, probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = P(57,000 < X bar < 58,000)
P(57,000 <= X bar <= 58,000) = P(X bar <= 58,000) - P(X bar < 57,000)
P(X bar <= 58,000) = P( <=
) = P(Z <= 2.67) = 0.99621
P(X < 57000) = P( <
) = P(Z < -10.67) = P(Z > 10.67)
This probability is that much small that it is very close to 0
Therefore, P(57,000 < X bar < 58,000) = 0.99621 - 0 = 0.99621 .
The service area of the cylinder is 42 square fts.
Two parallel bases joined by a curving surface make up the three-dimensional solid known as a cylinder.
Typically, the bases are shaped like circles. The height "h" of the cylinder stands for the perpendicular distance between the bases, while "r" stands for the cylinder's radius.
The uses of cylinder are-
- A popular piece of scientific equipment used to determine the volume of a liquid is a graduated cylinder, sometimes referred to as a measuring cylinder or mixing cylinder.
- Its form is slender and cylindrical. The measured amount of liquid is shown by each marked line on the graduated cylinder.
Total surface area of the cylinder formula:
It is the sum of the base surface area and the lateral surface area;
Total area = base area + lateral area , or
Total area = 2 π r² + (2 π r) h , or
Total area = 2 π r (r + h)
Calculation for the total area of the cylinder;
Base diameter is 6 ft
Radius is 6/2 = 3 ft
Height is 4 ft
Total area = 23(3 + 4)
= 6×7
= 42
Therefore, the total surface area of the cylinder is 42 square fts.
To know more about the surface area of the cylinder, here
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