Question

The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?

57

likes
284 views

Answer to a math question The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?

Expert avatar
Jon
4.6
108 Answers
Standardize the value of 58,000 km by subtracting the mean and dividing by the standard deviation. This gives us a z-score, which represents how many standard deviations the value is from the mean. The z-score for 58,000 km is given by: z = (58,000 - 64,000) / 9,000 β‰ˆ -0.67 The probability corresponding to z = -0.67 is approximately 0.7475. This means that there is a 74.75% chance that a single tire will last more than 58,000 km. Assuming independence between tires, we can simply raise the single-tire probability to the power of 4 to find this: P(all 4 tires > 58,000 km) = (0.7475)^4 β‰ˆ 0.3122 So, there is approximately a 31.22% chance that all 4 tires on a car will last more than 58,000 km.

Frequently asked questions (FAQs)
What is the domain of the cube root function?
+
In how many ways can 5 people be chosen and arranged out of a group of 10?
+
What is the derivative of f(x) = 3x^2 + 5x - 7 with respect to x?
+
New questions in Mathematics
𝑦 = ( π‘₯2 βˆ’ 3) (π‘₯3 + 2 π‘₯ + 1)
The derivative of a power is obtained just by subtracting 1 from the power True or false
58+861-87
x/20*100
Let I βŠ‚ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≀ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)
calculate the normal vector of line y = -0.75x + 3
A company that manufactures personal hygiene items purchases machinery for $220,000 that is considered to last 7 years; it is estimated that at the end of the period it will have a salvage value of $1000. Find: to. The depreciation rate. b. The book value at the end of the sixth year.
If 0101, what is the binary representation of the 4x16 decoder output?
sin 30
1. A capital of $3,831 was lent, and it has produced interest of $840 from 05-12-2022 to 1-12-2023. At what annual simple interest rate was the capital lent?
A teacher has 25 red and yellow counters altogether. She has 4 times as many red counters than yellow counters. How many yellow counters does the teacher have?
392929-9
Derivative of 2x
A loan is repaid with payments of $2226 made at the end of each month for 12 years. If interest on the loan is 5.2%, compounded semi-annually, what is the initial value of the loan? Enter to the nearest cent (two decimals). Do not use $ signs or commas.
8/9 divided by 10/6
An election ballot asks voters to select three city judges from a group of 12 candidates. How many ways can this be done?
The slope of the tangent line to the curve f(x)=4tan x at the point (Ο€/4,4)
Find the symmetric point to a point P = (2,-7,10) with respect to a plane containing a point Po = (3, 2, 2) and perpendicular to a vector u = [1, -3, 2].
A rectangular swimming pool has a length of 14 feet, a width of 26 feet and a depth of 5 feet. Round answers to the nearest hundredth as needed. (a) How many cubic feet of water can the pool hold? cubic feet (b) The manufacturer suggests filling the pool to 95% capacity. How many cubic feet of water is this? cubic feet
x(squared) -8x=0