Suppose X Is A Random Variable Best Described By A Uni

Suppose X Is A Random Variable Best Described By A Uni

Suppose x is a random variable best described by a uniform probability distribution with c EQUAL 30 and d EQUAL 90. Find P(30 ≤ x ≤ 45). Choose one answer. a. 0.15 b. 0.35 c. 0.25 d. 0.025

Which geometric shape is used to represent areas for a uniform distribution? Choose one answer. a. Rectangle b. Triangle c. Bell curve d. Circle

Find a value of the standard normal random variable z, called z0, such that P(-z0≤ z ≤ z0) EQUAL 0.98. Choose one answer. a. 2.33 b. 1.96 c. .99 d. 1.645

Suppose x is a random variable best described by a uniform probability distribution with c EQUAL 20 and d EQUAL 60. Find P(x > 60). Choose one answer. a. 0.4 b. 0.5 c. 1 d. 0

Suppose x is a random variable best described by a uniform probability distribution with c EQUAL 10 and d EQUAL 90. Find P(x

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 325 seconds. Choose one answer. a. .0107 b. .4893 c. .5107 d. .9893

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 3.5 to 5.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 4.6 millimeters? Choose one answer. a. 2 b. 0.8364 c. 0.5111 d. 0.45

Suppose x is a random variable best described by a uniform probability distribution with c EQUAL 3 and d EQUAL 9. Find the value of a that makes the following probability statement true: P(3.5 ≤ x ≤ EQUAL 0.5. Choose one answer. a. 6.5 b. 6 c. 4 d. 1.2

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 68°F to 90°F. What is the probability that the high temperature on a day in August exceeds 73°F? Choose one answer. a. 0.0455 b. 0.2273 c. 0.462 d. 0.7727

Suppose x is a random variable best described by a uniform probability distribution with c EQUAL 3 and d EQUAL 5. Find the value of a THAT makes the following probability statement true: P(x ≤ EQUAL 0.75. Choose one answer. a. 4.7 b. 4.5 c. 3.5 d. 1.5

For a standard normal random variable, find the probability that z exceeds the value -1.65. Choose one answer. a. 0.5495 b. 0.4505 c. 0.0495 d. 0.9505

Suppose x is a uniform random variable with c EQUAL 40 and d EQUAL 70. Find the standard deviation of x. Choose one answer. a. σ EQUAL 3.03 b. σ EQUAL 1.58 c. σ EQUAL 8.66 d. σ EQUAL 31.75

A machine is set to pump cleanser into a process at the rate of 7 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 9.5 gallons per minute. What is the probability that at the time the machine is checked it is pumping more than 8.0 gallons per minute? Choose one answer. a. .50 b. .25 c. .7692 d. .667

After a particular heavy snowstorm, the depth of snow reported in a mountain village followed a uniform distribution over the interval from 15 to 22 inches of snow. Find the standard deviation of the snowfall amounts. Choose one answer. a. 1.42 inches b. 18.5 inches c. 2.02 inches d. 4.08 inches

The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the probability that the next customer who walks through the door exceeds 50 years old. Round to the nearest ten-thousandth. Choose one answer. a. 0.3600 b. 0.7619 c. 0.8333 d. 0.2381

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 30 to 80. What is the mean outcome of this experiment? Choose one answer. a. 55 b. 30 c. 80 d. 60

Use the standard normal distribution to find P(-2.25

A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 11.5 gallons per minute. Find the probability that between 9.0 gallons and 10.0 gallons are pumped during a randomly selected minute. Choose one answer. a. 0 b. 0.33 c. 1 d. 0.67

Suppose x is a uniform random variable with c EQUAL 20 and d EQUAL 60. Find P(x > 44). Choose one answer. a. 0.4 b. 0.9 c. 0.6 d. 0.1

Find a value of the standard normal random variable z, called z0, such that P(z ≤ z0) EQUAL 0.70. Choose one answer. a. .47 b. .98 c. .53 d. .81

Paper For Above instruction

The understanding of probability distributions, particularly uniform and normal distributions, is fundamental in statistical analysis. These concepts enable us to characterize data and predict probabilities within specified parameters. This paper explores various problems involving uniform and normal distributions, calculating probabilities, standard deviations, and specific probability values, demonstrating practical applications in real-world scenarios including manufacturing, weather forecasting, and academic testing.

Uniform distribution, characterized by a constant probability over a specific interval, is efficient for modeling scenarios where each outcome within the range is equally likely. For example, the diameter of ball bearings produced in a factory can be modeled with a uniform distribution over a certain interval, reflecting the manufacturing process's consistency. In contrast, the normal distribution, a bell-shaped curve, describes variables like human height, test scores, or running times, where data cluster around a mean with a certain standard deviation. Both types of distributions support decision-making and quality control by quantifying the likelihood of various outcomes.

In addressing the uniform distribution problems, the calculation typically involves the formula for probability over an interval, P(a ≤ x ≤ b) = (b - a) / (d - c) when c and d define the minimum and maximum of the distribution. Standard deviation for uniform distributions is calculated as (d - c) / √12, reflecting the spread of the data. For example, in the case where the diameter of ball bearings ranges from 3.5 to 5.5 mm, the probability that a bearing exceeds 4.6 mm involves calculating the proportion of the distribution that falls above this value, which equals (5.5 - 4.6) / (5.5 - 3.5) = 0.45.

Normal distribution problems often require the use of Z-scores, which standardize a data point relative to the mean and standard deviation, enabling the use of standard normal tables or computational tools. For instance, to find the probability that a boy completes a mile run in less than 325 seconds, one would compute the Z-score as (325 - 440) / 50 = -2.25. Using the standard normal distribution table, P(Z

These statistical tools are vital in quality assurance, risk assessment, and operational planning. For example, predicting the probability of a machine pumping more than a certain amount of fluid aids in maintenance scheduling and process control. Similarly, the probability of snow accumulation exceeding specific depths helps in resource planning and emergency management. As modern industries increasingly rely on data-driven decision-making, mastering the application of these distributions remains essential for professionals across fields.

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