Business Week conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000 and for the female graduates it is $25,000. 1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why? 2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
Answers
Answer:
1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean
2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?
The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.
So
Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.
2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
We have that:
This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So
By the Central Limit Theorem
has a pvalue of 0.1587
15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Final answer:
1. We have a higher probability of obtaining a sample estimate within $10,000 of the population mean when the standard deviation is smaller. In this case, the standard deviation for female graduates is smaller, so the probability is higher. 2. The probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean can be calculated using the z-score formula and the z-table.
Explanation:
1. In the case where the standard deviation is smaller, we have a higher probability of obtaining a sample estimate within $10,000 of the population mean. This is because a smaller standard deviation indicates less variability in the data, making it more likely for the sample mean to be closer to the population mean. In this case, the standard deviation for female graduates is smaller, so the probability is higher.
2. To calculate the probability, we need to calculate the z-score and then use the z-table. The z-score formula is z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the given values, we find the z-score and use the z-table to find the probability.
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If m = 1/2, n= 1/4 , then m²+ n²
$500 shared in ratio 2:3:9
3 less than a number b divided by 2
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Answer:
Circumference=2πr or πd
So:
3.14 × 6cm
=18.84cm
c. What is the probability that the number of members in a typical household in India is strictly between 2 and 5? (Round your answer to 2 decimal places.)
Probability
Answers
The probability that the number of members in a typical household in India is less than 5, greater than or equal to 5, and strictly between 2 and 5 are 0.54, 0.46, and 0.43 respectively
Probability distribution
Given the probability distribution for the household size in India as shown;
X 1 2 3 4 5 6 7 8 Total
P 0.02 0.09 0.18 0.25 0.20 0.12 0.08 0.06 1.00
a) The probability that the number of members in a typical household in India is strictly less than 5 is given as:
P(X < 5) = P(X=1) + P(X=2) + P(X=3) + P(X=4)
P(X < 5) = 0.02+ 0.09 + 0.18 + 0.25
P(X < 5) = 0.54
b) The probability that the number of members in a typical household in India is greater or equal to 5 is given as:
P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8)
P(X ≥ 5) = 0.20 + 0.12 + 0.08 + 0.06
P(X ≥ 5) = 0.46
c) The the probability that the number of members in a typical household in India is strictly between 2 and 5
P(2 < X < 5) = P(X=3) + P(X=4)
P (2 < X < 5) = 0.18 + 0.25
P (2 < X < 5) = 0.43
Hence the probability that the number of members in a typical household in India is less than 5, greater than or equal to 5, and strictly between 2 and 5 are 0.54, 0.46, and 0.43 respectively
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Answer:
0.54,0.46,0.43
Step-by-step explanation:
Given that India is the second most populous country in the world, with a population of over 1 billion people.
The pdf of household size say X in India varies from 1 to 8.
The distribution is shown as follows
X 1 2 3 4 5 6 7 8 Total
P 0.02 0.09 0.18 0.25 0.20 0.12 0.08 0.06 1.00
a) the probability that there are less than 5 members in a household in India
=
=
b. the probability that there are 5 or more members in a typical household
in India
=
c) the probability that the number of members in a typical household in India is strictly between 2 and 5
Answers
Therefore, there will be 2 tiles left over.
Answers
The ratio of the number of cups of apple juice to the number of cups of lemon-lime soda is 6:1
What is the ratio?
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Given that x axis denotes Lemon lime soda in cups and y axis denotes Apple juice in cups
(x) Lemon -Lime Soda ; 0, 1, 2, 3, 4, 5
(y) Apple Juice : 0, 6, 12, 18, 24, 30
Therefore, the ratio can be written as;
the number of cups of apple juice : the number of cups of lemon-lime soda
6 : 1
Then, ratio is 6:1
Hence, the ratio of the number of cups of apple juice to the number of cups of lemon-lime soda is 6:1
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(y) Apple Juice 0, 6, 12, 18, 24, 30
number of cups of apple juice : the number of cups of lemon-lime soda
6 : 1
ratio is 6:1
Answers
Answer:
I believe the answer would be BC=3(EF)
Step-by-step explanation:
the action of moving back and forth quickly and steadily
the distance between one compression and the compression next to it
the action of moving through a material or substance
Answers
Answer:
the action of moving back and forth quickly and steadily
Explanation:
hopes this helps :D