Let Ф denote the standart normal distribution function. Then we need to find Ф(2.34), which we read from be table, and it is approximately equal to 0.9904=99.04%

Question

asked 2021-06-05

Use the following Normal Distribution table to calculate the area under the Normal Curve (Shaded area in the Figure) when \(Z=1.3\) and \(H=0.05\);

Assume that you do not have vales of the area beyond \(z=1.2\) in the table; i.e. you may need to use the extrapolation.

Check your calculated value and compare with the values in the table \([for\ z=1.3\ and\ H=0.05]\).

Calculate your percentage of error in the estimation.

How do I solve this problem using extrapolation?

\(\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}\)

Assume that you do not have vales of the area beyond \(z=1.2\) in the table; i.e. you may need to use the extrapolation.

Check your calculated value and compare with the values in the table \([for\ z=1.3\ and\ H=0.05]\).

Calculate your percentage of error in the estimation.

How do I solve this problem using extrapolation?

\(\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}\)

asked 2021-05-09

The annual profit for a company that manufactures cell phine accessories can be modeled by the function

\(\displaystyle{P}{\left({x}\right)}=-{0.0001}{x}^{{2}}+{70}{x}+{12500}\) where x is the number of units sold and P is the total profit in dollars.

a. What sales level maximizes the company's annual profit?

b. Find the maximum annual profit for the company.

\(\displaystyle{P}{\left({x}\right)}=-{0.0001}{x}^{{2}}+{70}{x}+{12500}\) where x is the number of units sold and P is the total profit in dollars.

a. What sales level maximizes the company's annual profit?

b. Find the maximum annual profit for the company.

asked 2021-05-04

Find the planes tangent to the following surfaces at the indicated points:

a) \(x^2+2y^2+3xz=10\), at the point (\(1,2,\frac{1}{3}\))

b) \(y^2-x^2=3\), at the point (1,2,8)

c) \(xyz=1\), at the point (1,1,1)

a) \(x^2+2y^2+3xz=10\), at the point (\(1,2,\frac{1}{3}\))

b) \(y^2-x^2=3\), at the point (1,2,8)

c) \(xyz=1\), at the point (1,1,1)

asked 2021-06-08

What is the domain of
\(\displaystyle{f{{\left({x}\right)}}}={5}\frac{{x}}{{{3}-{\left(\sqrt{{x}}-{2}\right)}}}\)?