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ladawnrowles005
28.03.2021 •
Mathematics
Someone please help these questions are due at 11;59 today please help urgent
1)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 258.5-cm and a standard deviation of 2.3-cm. For shipment, 30 steel rods are bundled together.
Find the probability that the average length of a randomly selected bundle of steel rods is between 258.5-cm and 259-cm.
P(258.5-cm < M < 259-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
2)
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 127.1-cm and a standard deviation of 1.6-cm. For shipment, 6 steel rods are bundled together.
Find P17, which is the average length separating the smallest 17% bundles from the largest 83% bundles.
P17 =
-cm
Enter your answer as a number accurate to 2 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
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Ответ:
1) P(258.5-cm < M < 259-cm) = 8.71%.
2) P17 = 125.57cm
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Question 1:
Mean of 258.5-cm and a standard deviation of 2.3-cm, which means that![\mu = 258.5, \sigma = 2.3](/tpl/images/1226/1509/2e501.png)
Find the probability that the average length of a randomly selected bundle of steel rods is between 258.5-cm and 259-cm.
This is the pvalue of Z when X = 259 subtracted by the pvalue of Z when X = 258.5.
X = 259
X = 258.5
0.5871 - 0.5 = 0.0871
0.0871*100% = 8.71%. So
P(258.5-cm < M < 259-cm) = 8.71%.
Question 2:
Mean of 127.1-cm and a standard deviation of 1.6-cm, which means that![\mu = 127.1, \sigma = 1.6](/tpl/images/1226/1509/c2085.png)
Find P17, which is the average length separating the smallest 17% bundles from the largest 83% bundles.
This is the 17th percentile, which is X when Z has a pvalue of 0.17. So X when Z = -0.954.
P17 = 125.57cm
Ответ:
80 miles were driven after
of the gas was used.
Step-by-step explanation:
The car gets 30 miles in one gallon and we have to calculate the miles driven after 2
gallons of gas was used.
We will use unitary method to solve this question.
∵ In one gallon of gas car runs = 30 miles
∴ In 8/3 gallons the car will cover the distance =
= 8×10 = 80 miles
Therefore the car will be driven 80 miles with
of gas.