Round 75.64 to the nearest ten
2 answers:
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Answer:
c. The number of 7's in a randomly selected set of five random digits from a table of random digits.
True, for this case we have a value fixed for n =5 and the probability is defined for each number 1/10 assuming numbers (0,1,2,3,4,5,6,7,8,9) so then the random variable "The number of 7's in a randomly selected set of five random digits" can be modelled with the binomial probability function.
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
The conditions to apply this distribution is that we have the parameters fixed n and p.
Let's analyze one by one the possible solutions:
a. The number of traffic tickets written by each police officer in a large city during one month.
False, the number of traffic tickets written by each police is not a fixed amount always, so then the value of n change and we can't apply a binomial model for this case.
b. The number of hearts in a hand of five cards dealt from a standard deck of 52 cards that has been thoroughly shuffled.
False, not all the hands of size 5 are equal and since we can't ensure this condition then the binomial model not apply for this case
c. The number of 7's in a randomly selected set of five random digits from a table of random digits.
True, for this case we have a value fixed for n =5 and the probability is defined for each number 1/10 so then the random variable "The number of 7's in a randomly selected set of five random digits" can be modelled with the binomial probability function.
d. The number of phone calls received in a one-hour period.
False, the number of phone calls change by the hour and is not always fixed so then we don't have a valu for n, and the binomial model not applies for this case.
e. All of the above.
False option C is correct.
Answer:
(a) C: 0.0465 ; reject the null hypothesis
(b) B: 0.3409 ; fail to reject the null hypothesis
Step-by-step explanation:
Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;
- If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.
- If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.
(a) Now, we are given alternate hypothesis, : p < 3/5
Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;
P-value = P(Z < -1.68) = 1 - P(Z 1.68)
= 1 - 0.95352 = <u>0.0465</u>
Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which <u>we reject the null hypothesis.</u>
(b) Now, we are given alternate hypothesis, : p > 0.383
Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;
P-value = P(Z > 0.41) = 1 - P(Z 0.41)
= 1 - 0.6591 = <u>0.3409</u>
Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which <u>we fail to reject the null hypothesis.</u>
The distance traveled by the particle is given by the definite integral
where