Ten people at a party decide to compare ages. Five people are 30 years old, three are 32, one is 31, and one is 65. Given the ag
2 answers:
Answer:
A. The mean age of the ten people at a party is: 34.2
B. The standard deviation is: 10.3066
Step-by-step explanation:
We are given a information about the age of ten people as:
Age(in years) Number of people
30 5
32 3
31 1
65 1
Hence, the mean of the age is calculated as:
Now, we calculate the standard deviation in the following steps:
x x-x' (x-x')²
30 -4.2 17.64
30 -4.2 17.64
30 -4.2 17.64
30 -4.2 17.64
30 -4.2 17.64
32 -2.2 5.06
32 -2.2 5.06
32 -2.2 5.06
31 -3.2 10.24
65 30.8 948.64
∑ (x-x')²= 1062.26
Variance=∑ (x-x')²/10=106.226
Hence, standard deviation is the square root of variance.
standard deviation is:
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Answer:
Possible values of dimensions are (24,16,2) or (24,8,4)
Step-by-step explanation:
We are given the volume of the Cuboid and length . We are required to find the possible values of width and height from this information.
Let us say that the width is x and height is y
Length = 24
Volume of a cuboid = length * width * height
Volume = 768
768=24*x*y
xy=32
Now the possible factors of 32
32=1*32 ( Which shall not be taken into consideration as length is already given as 24 and width or height can not be more length)
32=2*16
32=4*8
Hence the possible values width are 8, 16 and that of height 4 and 2
Hence the possible values of dimensions are (24,16,2) or (24,8,4)
The 4 subintervals are given: [2, 4], [4, 7], [7, 9], and [9, 10].
Each subinterval has length: 4 - 2 = 2, 7 - 4 = 3, 9 - 7 = 2, and 10 - 9 = 1.
Over each subinterval, we take the value of the function at the right endpoint: 3, 8, 15, and 18.
Then the integral is approximately
so 78.0 is the correct answer.
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:
The maximum profit can be attained when 4 bikes are produced each day.
Step-by-step explanation:
Look at the attached picture:
In the table given in the picture, the number of bikes produces varies. We cannot properly compare the profits per day. To be consistent, let us determine the profit per unit of bike produced.The relationship between cost, revenue and profit can be as:
Profit = Revenue - Cost
To find the profit per unit of bike, simply divide the profit with the number of bikes produced (1st column). After you see the results, we can see that the highest profit is $17.5 per unit of bike produced. Therefore, the maximum profit can be attained when 4 bikes are produced each day.
