Question

An electrical company manufactures batteries that have a duration that is distributed approximately normally, with a mean of 700 hours and a standard deviation of 40 hours. Find the probability that a randomly selected battery has an average life of less than 810 hours.

121

likes
604 views

Answer to a math question An electrical company manufactures batteries that have a duration that is distributed approximately normally, with a mean of 700 hours and a standard deviation of 40 hours. Find the probability that a randomly selected battery has an average life of less than 810 hours.

Expert avatar
Birdie
4.5
103 Answers
Para encontrar la probabilidad de que una batería seleccionada al azar tenga una vida útil promedio de menos de 810 horas, usaremos las propiedades de la distribución normal. Dado: Media (\( \mu \)) = 700 horas Desviación estándar (\( \sigma \)) = 40 horas Queremos encontrar \( P(X < 810) \), donde \( X \) representa la vida útil promedio de una batería. Primero, estandaricemos el valor 810 usando la fórmula de puntuación z: \[ Z = \frac \] Dónde: - \( X \) es el valor que nos interesa (810 horas). - \( \mu \) es la media (700 horas). - \( \sigma \) es la desviación estándar (40 horas). \[ Z = \frac \] \[ Z = \frac \] \[ Z = 2,75 \] Ahora que tenemos el puntaje z, usaremos una tabla de distribución normal estándar o una calculadora para encontrar la probabilidad correspondiente a este puntaje z. Según la tabla de distribución normal estándar o la calculadora, la probabilidad de que \( Z < 2,75 \) sea aproximadamente 0,9970. Por lo tanto, la probabilidad de que una batería seleccionada al azar tenga una vida promedio de menos de 810 horas es aproximadamente 0,9970 o 99,70%.

Frequently asked questions (FAQs)
What is the value of sin(45°) in terms of Trigonometric Ratios?
+
What is 60% of 125?
+
What is the slope (m) of a line passing through (-3, 2) and (5, 10)?
+
New questions in Mathematics
Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps
-442/c+5=26 what is c?
The sum of an infinite geometric series is 13,5 The sum of the same series, calculated from the third term is 1,5. Q. Calculate r if r>0.
3(2+x)-2(2x+6)=20-4x
Karina has a plot of 5,000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used for cultivation?
The bus one way of the road which is 10km is heading with speed of 20km/h ,then the bus the other 10km is heading with speed of 60km/h. The middle speed of the road is it equal with arithmetic speed of the v1 and v2 ?
Answer the following questions regarding the expression below. 0.1 (a) Write the number as a fraction.
Suppose the Golf ball market is perfectly competitive and the functions are known: Q = 120 – 2Px – 2Py 0.2I Q = 2Px 40 Where I = Consumers' income ($200) and Py = Price of Good Y (40) Calculate the equilibrium elasticity: a) 1.6 b) -6 c) 6 d) 0.6
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
Convert 5/9 to a decimal
Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.
A car travels 211 miles on 15 gallons of gasoline. The best estimate of the car’s miles per gallon is?
Determine a general formula​ (or formulas) for the solution to the following equation.​ Then, determine the specific solutions​ (if any) on the interval [0,2π). cos30=0
5x+13+7x-10=99
Write the detailed definition of a supply chain/logistics related maximization problem with 8 variables and 6 constraints. Each constraint should have at least 6 variables. Each constraint should have At least 5 variables will have a value greater than zero in the resulting solution. Variables may have decimal values. Type of equations is less than equal. Numbers and types of variables and constraints are important and strict. Model the problem and verify that is feasible, bounded and have at least 5 variables are nonzero.
Nancy is a waitress at Seventh Heaven Hamburgers. She wants to estimate the average amount each table leaves for a tip. A random sample of 5 groups was taken and the amount they left for a tip (in dollars) is listed below: $11.00 $8.00 $6.00 $3.00 $7.00 a.) Find a 90% confidence interval for the average amount left by all groups. (*round to the nearest cent*) $ < μ < $ b.) If the sample size were larger, with everything else remaining the same, would the margin of Error increase or decrease? Decrease Increase c.) If the Confidence level were 95% instead of 90%, would the range (size) of the Confidence Interval be larger or smaller? Larger Smaller
Let N be the total number of ways to choose at least one ride, out of a total of 7 different ones, existing in an amusement park. Can it be said that N is a natural number equal to?
How many cards do you expect to pull from a poker deck until you get an ACE?
Convert (324)𝑓𝑖𝑣𝑒 into base-ten
64-6x^2>0