Answer:
0.04
Step-by-step explanation:
In this case we must use the following formula to be able to find the standard error, which would be the square root, of the probability for its complement divided by the population:
SE=
Now, knowing that p = 0.552 and n = 160 we replace and we are left with:
SE =
SE =
SE = 0.039
Which means that the standard error of the proportion is 0.04
Answer:
0% probability that at least 1,500 will agree to respond
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the probability that at least 1,500 will agree to respond
This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So
has a pvalue of 1.
1 - 1 = 0
0% probability that at least 1,500 will agree to respond
Answer:
T = 3.967 C
Step-by-step explanation:
Density = mass / volume
Use the mass = 1kg and volume as the equation given V, we will come up with the following equation
D = 1 / 999.87−0.06426T+0.0085043T^2−0.0000679T^3
= (999.87−0.06426T+0.0085043T^2−0.0000679T^3)^-1
Find the first derivative of D with respect to temperature T
dD/dT =
Let dD/dT = 0 to find the critical value we will get
= 0
Using formula of quadratic, we get the roots:
T = 79.53 and T = 3.967
Since the temperature is only between 0 and 30, pick T = 3.967
Find 2nd derivative to check whether the equation will have maximum value:
Substituting the value with T=3.967,
d2D/dT2 = -1.54 x 10^(-8) a negative value. Hence It is a maximum value
Substitute T =3.967 into equation V, we get V = 0.001 i.e. the volume when the the density is the highest is at 0.001 m3 with density of
D = 1/0.001 = 1000 kg/m3
Therefore T = 3.967 C
Answer:
The correct option is 1.
Step-by-step explanation:
From the given histogram it is clear that
In age group 5-10, the number of students is 7.
In age group 11-13, the number of students is 5.
In age group 14-18, the number of students is 4.
It means age of 7 students lie in the interval 5-10, age of 5 students lie in the interval 11-13 and age of 4 students lie in the interval 14-18.
Total number of elements in the data set is
In option 3 and 4 number of elements is data set is less than 16. So, option 3 and 4 are incorrect.
In option 2 all the data set lie in the interval 5-10. So, option 2 is incorrect.
In option 1,
Class intervals elements frequency
5-10 5,6,7,8,9,10,10 7
11-13 11,11,12,12,13 5
14-18 14,14,15,16 4
From the above table we can conclude that data set 1 represented in the given histogram.
Therefore the correct option is 1.