A farmer cuts hazel twigs to make into beam poles to sell at the market.He says that the sticks are each 240cm long but in fact the lengths of the stick are normally distrinuted such that 55% of the sticks are longer than 240cm and 10% are longer than 250cm.Find the probability that a randomly selected stick is shorter than 235cm.
so P(x<240) = .45 and P(x < 250)= .9
(240-m)/s = -.125 and (250-m)/s = 1.282 , using http://davidmlane.com/normal.html
m - .125s = 240 and m + 1.282s = 250
subtract them:
1.407s = 10
s = 7.107, then m = 240.888
use the above webpage again, let me know what you got
I got 0.203 which is the answer.
I got the same
Btw, do you still use tables in the back of textbooks for these type of questions?
How are these taught in class these days, I have been retired for 23 years, so I am curious what happened to the old ways.
Only to calculate z values of area, we use calculators.But there is table given at the back if one wants to use it.
I use calculator.There is table at the back now also and student are provided table in the examinations.Its quite easier to deal with calculator than tables.
To calculate area we use calculator but to get z score of area we use the tables at back.
To find the probability that a randomly selected stick is shorter than 235cm, we need to calculate the area under the normal distribution curve from negative infinity up to 235cm.
First, let's find the mean and standard deviation of the stick lengths. We know that 55% of the sticks are longer than 240cm, so the mean will be greater than 240cm. Let's assume the mean is μ.
Next, we know that 10% of the sticks are longer than 250cm. This means that 90% of the sticks are shorter than or equal to 250cm. Using a standard normal distribution table or a calculator, we can find the z-score corresponding to the cumulative probability of 0.9, which is approximately 1.28 (rounded to two decimal places). The z-score is calculated using the formula (x - μ) / σ, where x is the value (250cm), μ is the mean, and σ is the standard deviation.
With the z-score, we can calculate the standard deviation as follows:
1.28 = (250 - μ) / σ
σ = (250 - μ) / 1.28
Now, we can set up the equation for the probability that a randomly selected stick is shorter than 235cm:
P(x < 235cm) = P(z < (235 - μ) / σ)
To solve this equation, we need to find the z-score corresponding to (235 - μ) / σ and then calculate the probability using the standard normal distribution table or a calculator.
Note: Since we do not have the specific values for the mean (μ) and standard deviation (σ) in this problem, we cannot determine the exact probability. However, if these values were provided, you could follow the steps outlined above to calculate the probability.