A craft store buys 50 yards of satin ribbon for 13.50. The store. The store sells the ribbon by the foot.A customer can purchase
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Answer:
The 95% confidence interval would be given by (0.380;0.441)
Step-by-step explanation:
In a study conducted in the United Kingdom about sleeping positions, 1000 adults in the UK were asked their starting position when they fall asleep at night. The most common answer was the fetal position (on the side, with legs pulled up), with 41% of the participants saying they start in this position. Use a normal distribution to find and interpret a 95% confidence interval for the proportion of all UK adults who start sleep in this position. Use the fact that the standard error of the estimate is 0.016
1) Notation and definitions
number of people who answer fetal position
random sample taken
estimated proportion of people who answer fetal position
true population proportion of people who answer fetal position
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
2) Confidence interval
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 (0.380;0.441)
Answer:
And we can find this probability with this difference:
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And we can use the z score formula given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference: