Let be the following probability density function f (x) = (1/3)[ e ^ {- x / 3}] for 0 <x <1 and f (x) = 0 in any other case
a) Determine the cumulative probability distribution F (X)
b) Determine the probability for P (0 <X <0.5)
In: Statistics and Probability
You are drawing 3 cards from a deck of 52.
a) What is the probability you draw an ace of spades, ace of hearts, and an ace of clubs in that order
b) What is the probability you draw 3 aces
c) what is the probability you draw 3 of a kind of any card.
In: Math
Among 16 electrical components exactly 4 are known not to function properly. If 6 components are randomly selected, find the following probabilities: (i) The probability that all selected components function properly. (ii) The probability that exactly 3 are defective. (iii) The probability that at least 1 component is defective.
In: Math
In: Chemistry
A bag of 29 tulip bulbs contains 12 red tulip bulbs, 8 yellow tulip bulbs, and 9 purple tulip bulbs.
(a) What is the probability that two randomly selected tulip bulbs are both red?
(b) What is the probability that the first bulb selected is red and the second yellow?
(c) What is the probability that the first bulb selected is yellow and the second red?
(d) What is the probability that one bulb is red and the other yellow?
(Round to three decimal places as needed.)
In: Statistics and Probability
IQ scores are normally distributed with a mean of 100 and a
standard deviation of 15.
A) If one person are randomly selected, find the probability the IQ
score is greater than 112.
B)If one person are randomly selected, find the probability the IQ
score is less than 95.
C)If one person are randomly selected, find the probability the IQ
score is between 97 and 110.
D) If 16 people are randomly selected, find the probability the IQ
score will be less than 95.
In: Statistics and Probability
A ultrasound technician (also known as diagnostic medical sonographers) have the knowledge and responsibility to perform ultrasound examinations utilizing a technology that creates detailed and dynamic images of the body's internal organs using high frequency sound waves. How can probability help these professionals perform their job duties?
(Be sure to include how probability is set up, what conclusions you can draw as you figure the probability, and any potential challenges in establishing probability statistics in your scenario).
In: Statistics and Probability
Vehicles entering an intersection from the east are equally likely to turn left, turn right, or proceed straight ahead. If 70 vehicles enter this intersection from the east, use technology and the normal approximation to the binomial distribution to find the exact and approximate probabilities of the following. (Round your answers to four decimal places.)
(a)
26 or fewer turn right
exact probability =
approximate probability =
(b)
at least two-thirds of those in the sample turn
exact probability =
approximate probability =
In: Statistics and Probability
Assume that light bulbs bought at a supermarket have a
probability 1/3 of being defective.
1）If you buy 10 light bulbs, what is the probability that 3 are
defective?
2）If you buy one light bulb per day, what is the probability
that the first defective one is on day three?
3）If you buy one light bulb per day, and the one bought on day one
was defective, what is the probability that the next defective one
is on day 5?
In: Statistics and Probability
The heights of American women 18 to 29 are normally distributed with a mean of 65 inches and a standard deviation of 3.5 inches. An American woman in this age bracket is chosen at random.
What is the probability that she is more than 68 inches stall?
What is the probability that she is less than 64 inches tall?
What is the probability that she is between 63 and 67 inches tall?
What is the probability that an American woman's height differs from the mean by more than 2.5 inches?
In: Statistics and Probability