17. BATTERY The life of a certain brand of AA battery is normally distributed with u = 8 hours and o = 1.5 hours. Find each probability. (Example 5) a. The battery will last less than 6 hours. b. The battery will last more than 12 hours. c. The battery will last between 8 and 9 hours.
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.
![Example 5 Find Probabilities
METEOROLOGY The temperatures for one month for a city in California are normally distributed
with u = 81° and o = 6°. Find each probability, and use a graphing calculator to sketch the
corresponding area under the curve.
a. P(70° < X< 90°)
The question is asking for the percentage of temperatures that were between 70' and 90°. First,
find the corresponding z-values for X = 70 and X = 90.
Formula for z-values
70 – 81
X=70, µ= 81, and a = 6
= -1.83
Simplify.
Use 90 to find the other z-value.
X - u
Formula for z-values
123
X = 90, µ=81, and o= 6
90 – 81
= 1.5
Simplify.
You can use a graphing calculator to display the area
that corresponds to any z-value by selecting 2nd [DISTR].
Then, under the DRAW menu, select ShadeNorm
(lower z value, upper z value). The area between
z = -1.83 and z = 1.5 is 0.899568, as shown.
Area=.899568
1ow= "1.83UP=1.5.
Therefore, approximately 90% of the temperatures were
between 70 and 90.
(-4, 4] scl: 1 by (0, 0.5] scl: 0.125](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48448195-1cd2-4ece-bd7d-0290c8233df5%2Ffe3c65af-2b43-44d2-af8f-6168ff219ec6%2Ftaq2pce_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
