Answer:
a) P(X<50)=0.9827
b) P(X>47)=0.4321
c) P(-1.5<z<1.5)=0.8664
Step-by-step explanation:
We will calculate the probability based on a random sample of one moped out of the population, normally distributed with mean 46.7 and standard deviation 1.75.
a) This means we have to calculate P(x<50).
We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:
b) We have to calculatee P(x>47).
We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:
c) If the value differs 1.5 standard deviations from the mean value, we have a z-score of z=1.5
So the probability that maximum speed differs from the mean value by at most 1.5 standard deviations is P(-1.5<z<1.5):
Answer:
The 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).
Step-by-step explanation:
A confidence interval is an interval estimate of the population parameter. The confidence interval has a certain probability of consisting the true value of the parameter.
The (1 - <em>α</em>) % confidence interval for the population proportion (<em>p</em>) is given by:
The information provided is:
*Use a <em>z</em>-table for the critical value.
Construct the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies as follows:
Thus, the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).
Answer:
3rd Option
Step-by-step explanation:
Which equation is the inverse of y = 7x2 – 10?
y = StartFraction plus-or-minus StartRoot x + 10 EndRoot Over 7 EndFraction
y = plus-or-minus StartRoot StartFraction x + 10 Over 7 EndFraction EndRoot
x = plus-or-minus StartRoot StartFraction x Over 7 EndFraction + 10 EndRoot
y = StartFraction plus-or-minus StartRoot x EndRoot Over 7 EndFraction plus-or-minus StartFraction StartRoot 10 EndRoot Over 7 EndFraction
Answer:
i) (0, 2) and (1, 2), ii) (0.333, 1.333) and (1, 2).
Step-by-step explanation:
i) Let be 
, if 
, which is equivalent to the following system of equations:
Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0, 2) and (1, 2)
ii) Let be , if 
, which is equivalent to the following system of equations:
Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0.333, 1.333) and (1, 2)
Answer:
a) p-hat (sampling distribution of sample proportions)
b) Symmetric
c) σ=0.058
d) Standard error
e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Step-by-step explanation:
a) This distribution is called the <em>sampling distribution of sample proportions</em> <em>(p-hat)</em>.
b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.
This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.
c) The variability of this distribution, represented by the standard error, is:
d) The formal name is Standard error.
e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:
If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
