Solving Probability Questions: Mean & CI Estimate

In summary, the conversation is about an engineer trying to estimate the mean setting time of a new cement mix used in highway spot repairs. The engineer has a record of setting times for 10 spot repairs and wants to find the mean and standard deviation of the setting time. They also want to find a 95% confidence interval for the mean setting time, assuming a known standard deviation of 1.5 minutes, and for an unknown standard deviation.
  • #1
sinni8
3
0
probability questions please help!

An engineer wishes to estimate the mean setting time of
a new cement mix used in highway spot repairs. From a record of setting times
for 10 spot repairs he obtain
x = 25; 25; 24; 23; 25; 26; 23; 24; 22; 23
minutes, respectively.
(a) Find the mean and standard deviation of the setting time.

(b) Find a 95% confidence interval for the mean setting time if the standard deviation
is known to be ¾ = 1:5 min: Assume a normal distribution
(c) Find a 95% confidence interval for for the mean setting time if the standard
deviation is unknown.
 
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  • #2
Welcome to PF!

sinni8 said:
An engineer wishes to estimate the mean setting time of
a new cement mix used in highway spot repairs. From a record of setting times
for 10 spot repairs he obtain
x = 25; 25; 24; 23; 25; 26; 23; 24; 22; 23
minutes, respectively.
(a) Find the mean and standard deviation of the setting time.

(b) Find a 95% confidence interval for the mean setting time if the standard deviation
is known to be ¾ = 1:5 min: Assume a normal distribution
(c) Find a 95% confidence interval for for the mean setting time if the standard
deviation is unknown.

Hi sinni8! Welcome to PF! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 

1. What is the difference between mean and CI estimate?

The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by summing all the values in the dataset and dividing by the total number of values. CI estimate, or confidence interval estimate, is a range of values that is likely to contain the true population mean with a certain level of confidence.

2. How is the mean calculated?

To calculate the mean, you add all the values in the dataset and divide by the total number of values. For example, if you have the values 5, 7, and 9, the mean would be (5+7+9)/3 = 7.

3. What does the confidence level in a CI estimate mean?

The confidence level in a CI estimate refers to the probability that the true population mean falls within the calculated confidence interval. For example, a 95% confidence level means that there is a 95% chance that the true population mean falls within the calculated interval.

4. How is a CI estimate calculated?

A CI estimate is calculated using the formula: CI = mean ± (critical value) * (standard deviation/√n), where the critical value is determined based on the desired confidence level and the standard deviation is a measure of the spread of the data.

5. How is probability related to mean and CI estimate?

Probability is the likelihood of a certain event occurring. In terms of mean and CI estimate, probability is used to determine the confidence level and the critical value needed to calculate the CI estimate. It is also used to interpret the results of the CI estimate, as it tells us the likelihood of the true population mean falling within the calculated interval.

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