Answer: The population proportion is between 0.34 and 0.46 .
Step-by-step explanation:
Interpretation of 95% confidence interval : A person can be about 95% confident that the true population parameter lies in the interval.
A confidence interval is constructed for an unknown population proportion, p. A sample is collected, and the 95% confidence interval is calculated to be 0.40 ± 0.06.
i.e. Lower limit =
Upper limit =
i.e. 95% confidence interval = (0.34, 0.46)
i.e. A person can be about 95% confident that the true population proportion (p) lies in the interval (0.34, 0.46).
⇒ It is most accurate to say that there is approximately 95% confidence in the assertion that:
The population proportion is between 0.34 and 0.46 .
Answer: 16. C 17. A 18. A
19 You got this! There is only one answer with the correct radius squared!
Step-by-step explanation:
For the coordinates of the center, flip the signs in the parentheses.
For the "=output": in the equation, square the given radius.
Center: (-14.4) the signs in (x + 14)²+(y - 4)² are the opposites.
Radius given: 2 Square it to get the =4
Answer: a) P = 0.5, b) P = 0.07
Step-by-step explanation:
Hi!
Lets call X₁ the time at which you arrive, and X₂ the time at which Bob arrives. Both are random variables with uniform density in the interval [0, 60] (in minutes). Their joint distribuition is uniform over the square in the image, with value P = 1/(60*60) = 1/3600.
a) For you to get more cake than Bob, you should arrive earlier. This event is A = { X₁ < X₂ }, the shaded triangle in the figure.The area of this event (set) is half the total area of the square, so P(A) = 0.5.
It makes sense, beacuse its equally probable for you or Bob to arrive earlier, as both have uniform density over the time interval.
b) In this case you arrive later than Bob, but less than 5 minutes later. So the event is B = { X₂ < X₁ < (X₂ + 5) } . This is the gray shaded area in b) part of the image. Its area is the difference two triangles (half square - blue triangle), then the probability is:
