That's a little messy :)
If that is: -1/[3^(n-1)]
-1, -1/3, -1/9, -1/27, -1/81
Answer:
For the first question the sample size is n= 3850


And replacing we got:


We are confident at 95% that the true proportion of all people who like the movie is between 0.484 and 0.516.
Step-by-step explanation:
We have the following info given:
represent the estimated proportion of all people who like the movie
represent the sample size selected
For the first question the sample size is n= 3850
For the second part they gives to us the margin of error:

We know that the confidence interval for a population proportion
of interest is given by:

And the margin of error is given by:

So then the confidence interval can be found with this formula:

And replacing we got:


We are confident at 95% that the true proportion of all people who like the movie is between 0.484 and 0.516.
Answer:
<u>The probability of drawing four red cards in a row (with replacement)is 0.1975</u>
Step-by-step explanation:
Assuming we have a standard card deck, we'll have this color distribution:
- Spades : Black
- Clubs : Black
- Diamonds : Red
- Hearts : Red
In consequence, if we remove all of the clubs from the deck, we will have 26 red cards out of 39 cards left.
Now, let's recall that the formula of probability is:
Probability = Number of favorable outcomes/Total number of possible outcomes
Replacing with the values we know:
- Probability of drawing a 1st red card = 26/39 = 2/3
- We return the 1st card to the deck, reshuffle and draw a new card:
- Probability of drawing a 2nd red card = 2/3
- We return the 2nd card to the deck, reshuffle and draw a new card:
- Probability of drawing a 3rd red card = 2/3
- We return the 3rd card to the deck, reshuffle and draw a new card:
- Probability of drawing a 4th red card = 2/3
Therefore,
Probability of drawing four red cards in a row (with replacement):
2/3 * 2/3 * 2/3 * 2/3 = 16/81
<u>16/81 = 0.1975</u>
Answer:
OPTION C
Step-by-step explanation:
To find the quotient of 
Multiplying and dividing by conjugate we get:


[Since,
]



Therefore, OPTION C is the answer.