Mean and standard deviation probability help

This gives a value of 3.0605 for sigma which is likely more accurate than the 3.75 you used. However, I am still getting a very similar answer as you.In summary, using the formula mu=p and sigma=sqrt(npq) for the mean and standard deviation of a sample proportion, the probability that the sample proportion will be greater than 0.34 is approximately 0.036. This probability was calculated using the z-table and the standardized normal random variable formula.
  • #1
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A department store has determined that 25% of all their sales are credit sales. A random sample of 75 sales is selected and the proportion of credit sales in the sample is computed.
a) What is the probability that the sample proportion will be greater than 0.34?

my answer is:
n=75 p=0.25
mu=np=18.75
sigma=sqrt(n*p*(1-p)) = 3/75

0.34 * 75=25.5

z=x-mu/sigma = 25.5-18.75/3.75 =1.8

P(z>1.8)=0.0359

the answer i got is 0.0359 but i am not confident, please tell me if i am correct or not. Thanks.
 
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  • #2
oh, i just found another equation for mean and standard deviation of a sample proportion is mu=p and sigma=sqrt(p(1-p)/n)
which one should i use for this question?
 
  • #3
One big thing:

The z-table in your book gives you P(z<Z) for a standardized normal random variable Z, not P(z>Z). So, P(z>1.8) = 1 - P(z<1.8) = 1 - phi(1.8). You may have already done that in your calculations but you did not specify that if you did.

The formula I have for sigma is: sqrt(npq) where q=(1-p).
 

What is the mean and standard deviation?

The mean, commonly known as the average, is the sum of all the data points divided by the number of data points. Standard deviation is a measure of how much the data values deviate from the mean. It is calculated by finding the square root of the sum of the squared differences between each data point and the mean.

Why are mean and standard deviation important in probability?

Mean and standard deviation are important in probability because they help us understand the distribution of data. The mean gives us a central point around which the data is spread, and the standard deviation tells us how spread out the data is. In probability, we use these measures to calculate the likelihood of events occurring.

How do you calculate mean and standard deviation?

To calculate the mean, add up all the data points and divide by the number of data points. To calculate the standard deviation, first find the mean. Then, for each data point, subtract the mean and square the result. Add up all the squared differences and divide by the number of data points. Finally, take the square root of this value to get the standard deviation.

What is the difference between population and sample mean and standard deviation?

Population mean and standard deviation are calculated using all the data points in a given population. Sample mean and standard deviation are calculated using a subset of data points from the population. Generally, population mean and standard deviation are used when we have data for the entire population, while sample mean and standard deviation are used when we have data for only a portion of the population.

How do mean and standard deviation affect the shape of a distribution?

The mean and standard deviation can tell us about the shape of a distribution. If the mean and standard deviation are close in value, the distribution will be more symmetrical and bell-shaped. If the mean and standard deviation are far apart, the distribution will be more spread out and skewed. Knowing the mean and standard deviation can also help us identify outliers in a distribution.

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