The diameters of bolts produced by a particular machine follow a normal distribution with mean 1.34cm and standard deviation 0.04cm.A bolt is rejected if its diameter is less than 1.24 or more than 1.40cm.i.Find the percentage of bolts which are accepted.
If the new mean is 1.32 , find the percentage of bolts that are rejected because they are too small in diameter.Sd remains same.
Use the link that I had given you before for other problems of this kind
http://davidmlane.com/normal.html
Just enter the mean and SD, click on between and enter the data
Let me know what your answer is, I got one
I got 0.927 which is required answer.
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.
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Correct for this one,
I also did the other one
To find the percentage of bolts that are accepted, we need to calculate the proportion of bolts that have a diameter between 1.24cm and 1.40cm.
Since we know that the diameters of bolts follow a normal distribution with mean 1.34cm and standard deviation 0.04cm, we can use the properties of the normal distribution to solve this problem.
Step 1: Find the z-scores for the lower and upper limits.
To calculate the z-scores, we use the formula: z = (x - μ) / σ, where x is the value (in this case, the lower or upper limit), μ is the mean, and σ is the standard deviation.
For the lower limit:
z1 = (1.24 - 1.34) / 0.04
For the upper limit:
z2 = (1.40 - 1.34) / 0.04
Calculating these values, we find:
z1 = -2.5
z2 = 1.5
Step 2: Find the area under the normal distribution curve between the z-scores.
We can now use a table of standard normal probabilities or a statistical calculator to find the area under the normal distribution curve between the z-scores.
Using a standard normal table or calculator, we find that the area to the left of z = -2.5 is approximately 0.0062, and the area to the left of z = 1.5 is approximately 0.9332.
Step 3: Calculate the percentage of bolts that are accepted.
The proportion of bolts that are accepted is equal to the area between the z-scores, which is the area to the left of z2 minus the area to the left of z1.
P(X between 1.24 and 1.40) = P(z1 < Z < z2) = P(Z < z2) - P(Z < z1)
P(X between 1.24 and 1.40) = 0.9332 - 0.0062
P(X between 1.24 and 1.40) ≈ 0.927
To convert this proportion to a percentage, we multiply by 100:
Percentage of bolts accepted = 0.927 * 100 = 92.7%
Therefore, approximately 92.7% of the bolts produced by the machine are accepted.