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professor190 [17]
2 years ago
15

In a shipment of toys from a manufacturer. The probability that a toy is defective is 1/50. If Marie selects 2 toys from a shipm

ent. What is the probability that both toys are defective?
Mathematics
2 answers:
GrogVix [38]2 years ago
8 0

Answer:  The required probability is \dfrac{1}{2500}.

Step-by-step explanation:  Given that in a shipment of toys from a manufacturer, where

the probability that a toy is defective is \frac{1}{50}.

We are to find the probability that both toys are defective, if Marie selects 2 toys from a shipment.

Since the events of selecting toys from a shipment are independent of each other,

therefore, the required probability that both toys are defective, if Marie selects 2 toys from a shipment will be

P=\dfrac{1}{50}\times\dfrac{1}{50}=\dfrac{1}{2500}.

Thus, the required probability is \dfrac{1}{2500}.

sukhopar [10]2 years ago
7 0
The probability is 1/2500. (1/50)*(1/50)
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The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a s
andrezito [222]

Answer:

a) Null hypothesis:p \leq 0.113  

Alternative hypothesis:p > 0.113  

b) z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing we got:

z=\frac{0.13 -0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}}=1.074  

The p value for this case would be given by:

p_v =P(z>1.074)=0.141  

c) For this case we see that the p value is higher than the significance level of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion workers belonged to unions is significantly higher than 11.3%

Step-by-step explanation:

Information given

n=400 represent the random sample taken

X=52 represent the  workers belonged to unions

\hat p=\frac{52}{400}=0.13 estimated proportion of workers belonged to unions

p_o=0.113 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic

p_v represent the p value

Part a

We want to test if the true proportion of interest is higher than 0.113 so then the system of hypothesis are.:  

Null hypothesis:p \leq 0.113  

Alternative hypothesis:p > 0.113  

Part b

The statistic is given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing we got:

z=\frac{0.13 -0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}}=1.074  

The p value for this case would be given by:

p_v =P(z>1.074)=0.141  

Part c

For this case we see that the p value is higher than the significance level of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion workers belonged to unions is significantly higher than 11.3%

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To solve for the system of equations, I will write the equation down as I rewrite the written form.
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Now let's write only what's in the parenthesis.
n + 3n -15 = 101.
The correctly written form in your answers is:
3n - 15 + n = 101, your first answer.
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