Suppose that 35% of all business executives are willing to switch companies if offered a higher salary. If a headhunter randomly contacts a simple random sample of 100 executives, what is the probability that over 40% will be willing to switch companies if offered a higher salary? (Choose the best/closest answer to account for minor rounding)- ○ .1469- ○ .1977- ○ .4207- ○ .8023- ○ .8531Question Help: Message instructor[Submit Question] button

Let Xi be a random variable such that Xi=1, if ith executive is willing to switcch0 otherwise Xi=1,…

Answered: bability that over 40% will be willing…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

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Suppose that 35% of all business executives are willing to switch companies if offered a higher salary. If a headhunter randomly contacts a simple random sample of 100 executives, what is the probability that over 40% will be willing to switch companies if offered a higher salary? (Choose the best/closest answer to account for minor rounding)

- ○ .1469
- ○ .1977
- ○ .4207
- ○ .8023
- ○ .8531

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Step 1

Let X_i be a random variable such that

X_i= $\{\begin{cases} 1, i f i^{t h} e x e c u t i v e i s w i l l i n g t o s w i t c c h \\ 0 o t h e r w i s e \end{cases}$

X_i= $\{\begin{cases} 1, w i t h p r o b a b i l i t y p = 0.35 \\ 0, w i t h p r o b a b i l i t y 0 (1 - p) = 0.65 \end{cases}$

X_i $~ B e r n o u l i (p = 0.35)$ , independently and identically distributed.

If $μ = E (X_{i}) a n d σ^{2} = V a r (X_{i}),$

then $μ = p = 0.35 a n d σ^{2} = p (1 - p) = 0.35 \times 0.65 = 0.2275 f o r a l l i = 1 (1) n$

Here, n=100 samples are selected.

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bability that over 40% will be willing to switch comp t/closest answer to account for minor rounding)