The amt of time cold sufferes will experience symptoms is normally distributed wiht a mean of 7.5 days and a standard deviation of 1.2 days what proportion of sufferers will experience in LESS THAN 4 days , also what proportion will experience sympotms for 7-10 days
How do you set these up? Thanks so much!
http://davidmlane.com/hyperstat/z_table.html use this, then figure with using your tables and check the result.
how do it on paper and pencil?
Get you tables. Figure the same thing on each limit. Your tables are made to read those numbers. If you don't understand, use some of the examples in your text.
To find the proportion of cold sufferers who will experience symptoms in less than 4 days, you need to calculate the z-score and use the standard normal distribution table. The z-score represents the number of standard deviations a data point is from the mean.
Step 1: Calculate the z-score
The formula for calculating the z-score is: z = (x - μ) / σ, where x is the value you want to find the proportion for, μ is the mean, and σ is the standard deviation.
For less than 4 days, x = 4, μ = 7.5, and σ = 1.2.
z = (4 - 7.5) / 1.2
Step 2: Use the z-score to find the proportion
Using the standard normal distribution table, look up the z-score you calculated in step 1. The table provides the proportion of data points that fall below that z-score.
Let's say the z-score corresponds to a proportion of P. To find the proportion of sufferers who will experience symptoms in less than 4 days, you subtract P from 0.5 (since the standard normal distribution table only provides values for the left side of the distribution).
The proportion of sufferers experiencing symptoms in less than 4 days would be 0.5 - P.
To find the proportion of sufferers who will experience symptoms for 7-10 days, you need to calculate the z-scores for both 7 and 10 days, and then use the table to find the proportion of data points falling between those z-scores.
Step 1: Calculate the z-scores
For 7 days, x = 7, μ = 7.5, and σ = 1.2.
z1 = (7 - 7.5) / 1.2
For 10 days, x = 10, μ = 7.5, and σ = 1.2.
z2 = (10 - 7.5) / 1.2
Step 2: Use the z-scores to find the proportion
Using the standard normal distribution table, look up the z-scores you calculated in step 1. The table provides the proportion of data points that fall to the left of those z-scores.
Let's say the z-scores correspond to proportions P1 and P2. To find the proportion of sufferers who will experience symptoms for 7-10 days, you subtract P1 from P2.
The proportion of sufferers experiencing symptoms for 7-10 days would be P2 - P1.
Using these steps, you can find the required proportions for the given scenarios.