probability that the member selected at random
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Question “probability that the member selected at random”
Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed.
Answer
Normal distribution:
Normal distribution is a continuous data distribution that follows a bell-shaped curve. The x normally distributed random variable has mean and standard deviation .
The standard normal distribution is a normal curve that has a mean of 0 and a standard deviation 1. The parameters of a normal distribution include mean as well as standard deviation .
Standardized z-score:
The standard z-score is the standard deviation of the data point from the mean.
* The z-score is positive if it is higher than the mean
* The z-score is a negative value if it falls below the mean
Let then find the z score using the formula below:
Where X is the individual raw score and denotes population mean, and denotes population standard deviation.
Formula to determine if X is more likely than a and less than b.
Let X be a random variable that indicates the braking distance in feet. It follows normal distribution with parametersand.
The bell-shaped curve can be derived from the information. The barking distance average is 168, and the standard deviation is 5.54. This is
, and . The x lower value is 160, and _ x higher is 168.
The Z-score is 160 when x is .
The Z-score is 168 when x is HTML1.
Below is the probability that the random member is selected from the shaded region of the graph.
the Z- score is 0, and the _z_scores are -1.44.
The probability required is
The “standard normal table” has an area to the right of
at 0.0749.
Ans:
This means that the probability of selecting the random member from the shaded region of the graph is 0.4251
Conclusion
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