Help me ..................

9966 [12]

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4 0

3 years ago

The caller times at a customer service center has an exponential distribution with an average of 22 seconds. Find the probabilit

jenyasd209 [6]

Answer:

The probability that a randomly selected call time will be less than 30 seconds is 0.7443.

Step-by-step explanation:

We are given that the caller times at a customer service center has an exponential distribution with an average of 22 seconds.

Let X = caller times at a customer service center

The probability distribution (pdf) of the exponential distribution is given by;

$f(x) = \lambda e^{-\lambda x} ; x > 0$

Here, $\lambda$ = exponential parameter

Now, the mean of the exponential distribution is given by;

Mean = $\frac{1}{\lambda}$

So, $22=\frac{1}{\lambda}$ ⇒ $\lambda=\frac{1}{22}$

SO, X ~ Exp( $\lambda=\frac{1}{22}$ )

To find the given probability we will use cumulative distribution function (cdf) of the exponential distribution, i.e;

$P(X\leq x) = 1 - e^{-\lambda x}$ ; x > 0

Now, the probability that a randomly selected call time will be less than 30 seconds is given by = P(X < 30 seconds)

P(X < 30) = $1 - e^{-\frac{1}{22} \times 30}$

= 1 - 0.2557

= 0.7443

7 0

3 years ago

The town of Hayward (CA) has about 50,000 registered voters. A political research firm takes a simple random sample of 500 of th

timama [110]

Answer: (0.076, 0.140)

Step-by-step explanation:

Confidence interval for population proportion (p) is given by :-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ = sample proportion.

n= sample size.

$\alpha$ = significance level .

$z_{\alpha/2}$ = critical z-value (Two tailed)

As per given , we have

sample size : n= 500

The number of Independents.: x= 54

Sample proportion of Independents $\hat{p}=\dfrac{x}{n}=\dfrac{54}{500}=0.108$

Significance level 98% confidence level : $\alpha=1-0.98=0.02$

By using z-table , Critical value : $z_{\alpha/2}=z_{0.01}=2.33$

The 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters will be :-

$0.108\pm (2.33)\sqrt{\dfrac{0.108(1-0.108)}{500}}\\\\=0.108\pm2.33\times0.013880634\\\\=0.108\pm0.03234187722\\\\\approx0.108\pm0.032=(0.108-0.032,\ 0.108+0.032)=(0.076,\ 0.140)$

Hence, the 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters.= (0.076, 0.140)

8 0

3 years ago

With what radius will a circle with a central angle

Vinil7 [7]

Answer:

no

Step-by-step explanation:

3 0

3 years ago

On a local sports team 20% of 50 players are left-handed how many left-handed players are on the team

mr Goodwill [35]

Answer:

10 players

Step-by-step explanation:

so a percentage is really just like a fraction or decimal so were going to turn it into a decimal by moving the decimal point two places to the left making it .20 then to figure out the answer we're going to multiply 50 by .20 to get 10

3 0

2 years ago

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