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Leya [2.2K]
3 years ago
12

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

Mathematics
1 answer:
Vinvika [58]3 years ago
4 0

Answer:

The point estimate for population mean is 8.129 Mpa.

Step-by-step explanation:

We are given the following in the question:

Data on flexural strength(MPa) for concrete beams of a certain type:

11.8, 7.7, 6.5, 6.8, 9.7, 6.8, 7.3, 7.9, 9.7, 8.7, 8.1, 8.5, 6.3, 7.0, 7.3, 7.4, 5.3, 9.0, 8.1, 11.3, 6.3, 7.2, 7.7, 7.8, 11.6, 10.7, 7.0

a) Point estimate of the mean value of strength for the conceptual population of all beams manufactured

We use the sample mean, \bar{x} as the point estimate for population mean.

Formula:

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

\bar{x} = \dfrac{\sum x_i}{n} = \dfrac{219.5}{27} = 8.129

Thus, the point estimate for population mean is 8.129 Mpa.

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Given the probability distributions shown to the​ right, complete the following parts.
Elan Coil [88]

Answer:

a) Expected Value for distribution A, E(X) = 3.020

Expected Value for distribution B, E(X) = 0.980

b) Standard deviation of distribution A = 1.157

Standard deviation of distribution B = 1.157

c) In distribution A, the bigger values of x have a higher probability of occurring than the values of distribution B (whose smaller values of x have a higher chance of occurring, hence, the expected value for distribution A is more than that of distribution B.

But according to the corresponding distribution of values, the two distributions have the same exact spread, A in ascending order (with higher values with bigger probability) and B in descending order (lower values have higher probabilities). But the same spread regardless, hence, the standard deviation which shows how data values spread around the mean (centre point) of a distribution is the same for the two distributions.

Step-by-step explanation:

Expected values is given as

E(X) = Σ xᵢpᵢ

where xᵢ = each possible sample space

pᵢ = P(X=xᵢ) = probability of each sample space occurring.

Distributions A and B is given by

X P(X) X P(x)

0 0.04 0 0.47

1 0.09 1 0.25

2 0.15 2 0.15

3 0.25 3 0.09

4 0.47 4 0.04

For distribution A

E(X) = Σ xᵢpᵢ = (0×0.04) + (1×0.09) + (2×0.15) + (3×0.25) + (4×0.47) = 3.02

For distribution B

E(X) = Σ xᵢpᵢ = (0×0.47) + (1×0.25) + (2×0.15) + (3×0.09) + (4×0.04) = 0.98

b) Standard deviation = √(variance)

But Variance is given by

Variance = Var(X) = Σx²p − μ²

where μ = E(X)

For distribution A

Σx²p = (0²×0.04) + (1²×0.09) + (2²×0.15) + (3²×0.25) + (4²×0.47) = 10.46

Variance = Var(X) = 10.46 - 3.02² = 1.3396

Standard deviation = √(1.3396) = 1.157

For distribution B

Σx²p = (0²×0.47) + (1²×0.25) + (2²×0.15) + (3²×0.09) + (4²×0.04) = 2.30

Variance = Var(X) = 2.30 - 0.98² = 1.3396

Standard deviation = √(1.3396) = 1.157

c) In distribution A, the bigger values of x have a higher probability of occurring than the values of distribution B (whose smaller values of x have a higher chance of occurring, hence, the expected value for distribution A is more than that of distribution B.

But according to the corresponding distribution of values, the two distributions have the same exact spread, A in ascending order (with higher values with bigger probability) and B in descending order (lower values have higher probabilities). But the same spread regardless, hence, the standard deviation which shows how data values spread around the mean (centre point) of a distribution is the same for the two distributions.

7 0
3 years ago
Please help with the question
Artyom0805 [142]

I find it convenient to look at the differences and the rate at which those differences are made up.

8. Jim is closing the $150 gap at the rate of $7.50 per week. He will catch up in

... 150/(7.5/week) = 20 weeks

9. At noon, the price of Stock A has increased by 0.05×3 = 0.15, so is now $15.90, which is $0.63 more than Stock B at that time. The prices are closing the gap at the rate of $0.05 +0.13 = $0.18 per hour, so will be the same after

... $0.63/($0.18/hour) = 3.5 hours . . . . after noon, at 3:30 pm

_____

You can also write and solve equations for the prices of the stocks. Or you can use a graphing calculator to tell you the solution. When equations are involved, I like to solve them the simplest possible way: let technology do it.

You are given the value at a time, and the rate of change of that value, so the equations are easily written in point-slope form. You will note that the common price at 3:30 pm (15.5 hours after midnight) is one that is not a whole number of cents. (That's usually OK for when trading stocks.)

4 0
3 years ago
The gas tank of Wendy’s car was 23 full. She used 16 of a tank of gas when driving to and from work. Which equation shows how fu
liberstina [14]

Answer:

The 3rd choice: 2/3 tank - 1/6 tank = 1/2 tank

Step-by-step explanation:

I assume those numbers are fractions.

The gas tank of Wendy’s car was 2/3 full. She used 1/6 of a tank of gas when driving to and from work. Which equation shows how full the gas tank is now?

We subtract 1/6 from 2/3. We need to use the common denominator 6.

2/3 - 1/6 = 4/6 - 1/6 = 3/6

Now we reduce 3/6.

2/3 - 1/6 = 1/2

Answer: 2/3 tank - 1/6 tank = 1/2 tank

7 0
3 years ago
12. Lydia is painting flower vases. Each vase takes 3⁄16 of a quart of paint. She has 21⁄2 quarts of paint. How many flower vase
neonofarm [45]
As we may be dividing fractions...
\frac{21}{2}  \div  \frac{3}{16}  =  \frac{21}{2} \times  \frac{16}{3}  =  \frac{7}{1} \times  \frac{8}{1}   = 56

5 0
3 years ago
If a chicken weight is 3 3/4 pounds, how many ounces those it has?
Dovator [93]

Answer:

60 ounces

Step-by-step explanation:

5 0
2 years ago
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