Given:
The initial mass of an element is 800 grams.
Decay rate = 8.2% per day
Number of days = 15
To find:
The remaining element after 15 days.
Solution:
The exponential decay model is
Where, a is the initial value r is the rate of interest and t is time period.
Putting in the above formula, we get
Therefore, the mass of the remaining element is 221.7 grams.
Answer:
a) For this case the value of the significanceis and
, we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:
If the calculated statistic we can reject the null hypothesis at 5% of significance
b) Where
c)
d) Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.
Step-by-step explanation:
Data given and notation
represent the number of people with the characteristic 1
represent the number of people with the characteristic 2
sample 1 selected
sample 2 selected
represent the proportion estimated for the sample 1
represent the proportion estimated for the sample 2
represent the pooled estimate of p
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
a.State the decision rule.
For this case the value of the significanceis and
, we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:
If the calculated statistic we can reject the null hypothesis at 5% of significance
b. Compute the pooled proportion.
Where
c. Compute the value of the test statistic.
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Replacing in formula (1) the values obtained we got this:
d. What is your decision regarding the null hypothesis?
Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.
Answer:
a) The mean is
b) The standard deviation is
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions 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.
The probability a student selected at random takes at least 55.50 minutes to complete the examination equals 0.6915.
This means that when X = 55.5, Z has a pvalue of 1 - 0.6915 = 0.3085. This means that when
So
The probability a student selected at random takes no more than 71.52 minutes to complete the examination equals 0.8997.
This means that when X = 71.52, Z has a pvalue of 0.8997. This means that when
So
Since we also have that
Question
The mean is
The standard deviation is