Answer:
The 95% confidence interval would be given by (0.027;0.093)
A. 0.027 to 0.093.
Step-by-step explanation:
Notation and definitions
number of defective.
random sample taken
estimated proportion of defectives
true population proportion of defectives
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by 
and 
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 95% confidence interval would be given by (0.027;0.093)
A. 0.027 to 0.093.
Let x be the rate of the slower bicyclist and
x + 4 be the rate of the faster bicyclist
Since the bicyclists are headed towards opposite directions, the sum of the distances they covered traveling for one hour and 15 minutes should be equal to 40 km based on the given conditions above. This may be expressed as,
(x)(1.25) + (x + 4)(1.25) = 40
Calculating gives x = 14
Thus, the rate of the bicyclists are 14 km/h and 18 km/h.
Answer:
f = 0
x > 2y
x ≤ 8
S ≥ 18
Step-by-step explanation:
Let 'f' represent the number of free throws.
Let 'x' represent the number of 2 - point baskets.
Let 'y' represent the number of 3 - point baskets.
Let S represent the Season high.
1) Ryan says he did not shoot any free throws.
⇒ f = 0
2) 2 - point baskets more than twice the number of 3 - point baskets.
⇒ x > 2y
3) Number of two points is less than or equal to 8.
⇒ x ≤ 8.
4) Last Season high, he had scored 18 points. Note that the problem says, Ryan equaled or bettered than last season high. That means he should got at least 18 points this season. So, the equation would be:
S ≥ 18
