The sides of a rectangle are scaled to be 1/4 of their original size

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean leng

alexandr402 [8]

Complete Question

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval obtain:

a. A point estimate of $\mu$ and its 90% margin of error.

b. A 95% confidence interval for $\mu$ .

Answer:

a

$\= x = 13.4$ . $E = 2.3$

b

$10.7 < \mu < 16.1$

Step-by-step explanation:

From the question we are told that

The sample size is n = 18

The 90% confidence interval is (11.1, 15.7)

Generally the point estimate of $\mu$ is mathematically evaluated as

$\= x = \frac{11.1 + 15.7 }{2}$

=> $\= x = 13.4$

Generally the margin of error is mathematically evaluated as

$E = \frac{15.7 - 11.1}{2 }$

=> $E = 2.3$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the equation for the lower limit of the confidence interval is

$\= x - Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{18} } = 11.1$

=> $13.4 - 0.3877 s = 11.1$

=> $s = 5.932$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * \frac{5.932}{\sqrt{18} }$

=> $E = 2.7$

Generally 95% confidence interval is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $13.4 - 2.7 < \mu < 13.4 + 2.7$

=> $10.7 < \mu < 16.1$

3 0

3 years ago

Help pls ill give briniest

Tems11 [23]

Answer:

4. a) kilometer

b) liter

5. a) gram

b) meter

I'm not totally sure if I'm right

5 0

3 years ago

Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p

Damm [24]

Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

Answer:

Number of t-shirts to make maximum profit = 2790 shirts

Maximum profit = $12,209

Step-by-step explanation:

From the question, we are given that the profit function is;

p(x) = -x³ + 4x² + x

For the maximum value of the profit function,

(dp/dx) = 0 and (d²p/dx²) < 0

Since, p(x) = -x³ + 4x² + x

Then,

(dp/dx) = -3x² + 8x + 1

at maximum point (dp/dx) = 0, thus;

-3x² + 8x + 1 = 0

Solving this using quadratic formula, the roots are;

x = -0.12 or 2.79

Also, (d²p/dx²) = -6x + 8

Now, let's put the roots of x into -6x + 8 and check for maximum value conditon;

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

Maximum has to be d²p/dx² < 0

So, the one that meets the condition is -8.74 < 0 at x = 2.79

Thus, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousands) = 2790

Now, the maximum profits that corresponds to this number of t-shirts of 2.79(in thousands) is obtained by putting 2.79 for x in the profit function;

So,

p(2.79) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.7176 + 31.1364 + 2.79

p(x) = 12.2088 (in thousand dollars) ≈ $12,209

6 0

3 years ago

Express a^6n/a^3n with positive exponents

Nat2105 [25]

I hope this helps you

a^6n-3n

a^3n

7 0

3 years ago

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the number of cars on equally Arbor Road in here 2007 was 2500 in Year 2014 the number is 4000 calculate the percentage increase

Zepler [3.9K]

Answer:

(4000/2500)100=160%

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3 years ago