Activity 2.2 The Average time it takes a group of senior high school students to complete a certain examination is 46.2 minutes. The Standard deviation is 8 minutes. Assume the variable is normally distributed. A. What is the probability that a random selected senior high student will complete the examination in less than 43 minutes? B. If 50 randomly selected senior high school students take the examination, what is the nrohahil
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![Activity 2.2
The Average time it takes a group of senior high school students to complete a
certain examination is 46.2 minutes, The Standard deviation is 8 minutes. Assume he
variable is normally distributed.
A. What is the probability that a random selected senior high student will
complete the examination in less than 43 minutes?
B. If 50 randomly selected senior high school students take the examination,
what is the probability that the mean time it takes the group to complete the
test will be less than 43 minutes?
The Central Limit Theorem is of fundamental importance in statistics because
it justifies the use of normal curve methods for a wide range of problems. This theorem
applies automatically to sampling from infinite population. It also assures that no
matter what the shape of the population distribution of the mean is, the sampling
distribution of the sample means is closely normally distributed whenever n is large.
Consequently, it justifies the use of the formula z =
when computing for
the probability that X will take on a value within a given range in the sampling
distribution of X.
z =
Where X = sample mean
p = population mean
D = population standard deviation
n = sample size
Activity 2.3
The average number of milligrams (mg) of cholesterol in a cup of a
certain brand of ice cream is 660 mg, and the standard deviation is 35 ma.
Assume the variable is normally distributed.
A. If a cup of ice cream is selected, what is the probability that the
cholesterol content will be more than 670 mg?
B. I a sample of 10 cups of ice cream is selected, what is the probability
that the mean of the sample will be larger than 670 mg?
An electric company claims that the average life of the bulbs it manufactures is
1200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs
is chosen, what is the probability that the sample mean will be:
a. greater than 1 150 hours?
b. less than 1 250 hours?
Activity 2.4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35cfb8e9-8563-470b-873b-022b189919a0%2F0282c0f0-e647-4e79-ad2f-4f870ac8cce0%2F1ompufi_processed.jpeg&w=3840&q=75)
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