Assume that when adults with smartphones are randomly selected, 57% use them in meetings or classes. If 5 adult smartphone users are randomly selected, find the probability that at least 3 of them use their smartphones in meetings or classes.

desireegarvin
2022-03-22

Assume that when adults with smartphones are randomly selected, 57% use them in meetings or classes. If 5 adult smartphone users are randomly selected, find the probability that at least 3 of them use their smartphones in meetings or classes.

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asked 2022-03-27

Deriving the confidence interval

$P(-{\mathrm{\Phi}}_{\alpha}^{-1}<X<{\mathrm{\Phi}}_{\alpha}^{-1})=1-2\alpha$

Let $P\sim \mathcal{N}(0,1)$

$\begin{array}{rlrlr}& P(-{\mathrm{\Phi}}_{\alpha}^{-1}X{\mathrm{\Phi}}_{\alpha}^{-1})& & & \left(1\right)\\ & P(X{\mathrm{\Phi}}_{\alpha}^{-1})-P(X-{\mathrm{\Phi}}_{\alpha}^{-1})& & P(AXB)=P(XB)-P(XA)& \left(2\right)\\ & \mathrm{\Phi}\left({\mathrm{\Phi}}_{\alpha}^{-1}\right))-\mathrm{\Phi}(-{\mathrm{\Phi}}_{\alpha}^{-1}\left)\right)& & P(XA)=\mathrm{\Phi}\left(A\right)& \left(3\right)\\ & \mathrm{\Phi}\left({\mathrm{\Phi}}_{\alpha}^{-1}\right))-(1-\mathrm{\Phi}\left({\mathrm{\Phi}}_{\alpha}^{-1}\right)\left)\right)& & \mathrm{\Phi}(-x)=1-\mathrm{\Phi}\left(x\right)& \left(4\right)\\ & \alpha -1+\alpha & & f\left({f}^{-1}\right)=id& \left(5\right)\\ & {-}{1}\times (1-2\alpha )& & & \left(6\right)\end{array}$

asked 2022-05-20

1a.

Show from first principles, i.e., by using the definition of linear independence,

that if μ = x + iy, y ̸= 0 is an eigenvalue of a real matrix

A with associated eigenvector v = u + iw, then the two real solutions

Y(t) = eat(u cos bt − wsin bt)

and

Z(t) = eat(u sin bt + wcos bt)

are linearly independent solutions of ˙X = AX.

1b.

Use (a) to solve the system (see image)

asked 2022-05-11

$f(x)=7{x}^{2}\ufeff+2$ and $g(x)=5{x}^{3}+7{x}^{2}+6x$, find the derivative of the quotient $\frac{f(x)}{g(x)}$.

asked 2022-02-28

Consider the incomplete character table for a group given below:

$$\begin{array}{|cccccc|}\hline & (1)& (1)& (2)& (2)& (2)\\ & 1& a& b& c& d\\ {x}_{1}& 1& 1& 1& 1& 1\\ {x}_{2}& 1& 1& -1& -1& 1\\ {x}_{3}& 1& 1& -1& -1& -1\\ {x}_{4}& 2& -2& 0& 0& 0\\ \hline\end{array}$$

All the conjugacy classes are there.

1) What is the order of the group?

2) How many characters are missing?

3) Find the missing character and complete the table.

4) Find the order of the Kemel of the missing character.

asked 2022-05-09

An MP3 manufacturer claimsthat 65% of teenagers 13 to 16 years old have their own MP3 players.

A researcher wishes to test the claim and selects a random sample of 80 teenagers. She finds that

57 have their own MP3 players. At � = 0.05, should the claim be rejected?

asked 2022-03-28

Find k$k$ such that the following matrix M$M$ is singular.

M=⎡⎣⎢−225+k−5933−4114⎤⎦⎥

asked 2022-05-13

set-builder form {y I x is a natural number and y >2}