Ask a Question? Get an Answer!
Question: A machine produces bolts, of which 10% are defective. Find the probability that in a random sample of 400 bolts produced by the machine, between 35 and 45 will be defective. Assume a standard deviation of 6. Steps to derive 1 The probability for a bolt to be defective, p 1 10 q p 9 10 n 2 n·p 1 10 n·q 9 10 3 Mean, μ = n·p 1 10 4 Standard Deviation, σ = n ⋅ p ⋅ q 4 0 0 × 1 1 0 × 9 1 0 5 Write the problem in probability notation: P (35 ≤ x x 6 P (35 - 0.5 < x x 7 The corresponding area under the normal curve distribution is shown in the diagram.8 The z 1 value corresponding to x z 1 = ( x - μ ) σ ( 3 4 . 5 - 4 0 ) 6 5.5 6 9 Similarly, the z 2 value corresponding to x z 2 = ( x - μ ) σ ( 4 5 . 5 - 4 0 ) 6 5.5 6 10 The area between z z 1 = - 0.9167 is 0.3203 by referring to the table for the probability z z z 2 = + 0.9167 is 0.3203.11 From the diagram, the probability for z z 1 and z 2 = the area for z 1 + the area for z 2 = 0.3203 + 0.3203 = 0.6406.12 So, the probability that between 35 and 45 will be defective is 0.6405.Hence the right answer is Option B Click Here To Go Back Find the number of ways of choosing 12 cards that contain exactly 8 red cards and 4 black.. If nC2 = 21, then the value of n is.. There are two parallel lines. 8 points are marked on one and 5 on the other. How many tri.. In how many different ways can an international committee of 5 be formed out of 6 American.. A question paper consists of two sections. There are 4 questions in the 1st section and 3 .. A man has 5 friends. In how many ways can he invite one or more of them for lunch?.. Find the number of ways of dividing 12 distinct books into 3 groups of 5, 4, 3 books respe.. If nC4 = nC3, then the value of n is:.. 36 games were played at a chess tournament with each contestant playing once against each .. nCr + nCr+1 = ?.. nPrnCr = ?.. Find Sin-1 (1) ... Find the value of Arccos (22)... Find the value of Sin-1(12)... Find Tan-13 ... Find Arcsec (2)... Find the value of Arccsc (2)... Find the value of sec-1(-1)... Find the value of Arccos (0.6157)... Find the value of Arctan (1.1106)... Find the value of Sin-1 (0.1218)... Find the value of Sin-1 (sin (-π3)) ... Find Tan-1[tan (3π4)]... Find the value of cos [Cos-1(35)]... Find the value of tan [Arccos(35)]... Find the value of sec [tan-1 (125)]... Find the value of csc [cot-1(724)]... tan [Sin-1 (- 513)] = ______ ... Find the value of sin [cos-1 (- 35)]... Find the value of Sin-1 (cosπ3)... Find the value of Cot-1 (sinπ2)... Find the value of sin (π4 + cos-1 (22))... Find the value of cos (π3 + Tan-1 (1))... Find the value of cot[Csc-1(2) - Sec-1(2)]... Find the value of sin [Tan-1 (34) + Sin-1 (1213)] ... Find the value of Tan-1 (x) + Cot-1 (x)... Find the value of Arccos (1213) + Arctan (125)... Find the value of cos [π2- sin-1 (-12)] ... Find the value of sin-1 (1 - 2sin2 θ)+ cos-1 (2cos2&nb.. Find the value of sin (2 cos-1 (35))... Find the value of cos [2 tan-1(17)]... Use the double-angle formula to find the value of sin 90°... Use the double-angle formula to find the value of cos 120°... The value of sin 300° is _______.. The value of tan 240° is _______ ... Use the double angle formula to find the value of tan 120°... If sin θ = 725 and θ is in first quadrant, then find the exact value of cos 2&.. If sin A = 35 and 0° < ∠A < 90°, then what is the value of sin 2A?.. If 90° < ∠B < 180° and sin B = 1213, then find the value of tan 2B... If tan B = - 13 and 90° < ∠B < 180°, then find the value of cos 2B... If ∠C is in fourth quadrant and cos C = 2425, then find the value of cos 2C... Use half-angle formula to find the value of sin 15°... Find the exact value of cos 75° using half angle formula... Find the exact value of tan 150° using half-angle formula... If 0° < θ < 90° and sin θ = 1213, then find the exact value of s.. If 90° < ∠ B < 180° and sin B = 45, then find the exact value of cos B2... If ∠ A is in third quadrant and cos A = - 513, then find the exact value of cos A2... If 270° < ∠ C < 360° and cos C = 35, then find the value of tan C2... Evaluate cos 22.5° using half-angle formula... Evaluate sin 67.5°... The value of tan 202.5° is ________.. Evaluate cos 112.5°... If 180° < θ < 270° and cos θ = - 2425, then the exact value of s.. Choose a formula that corresponds to the value of cos 4θ... Using double-angle formulas, choose the formula that corresponds to the value of sin 6&the.. Using double-angle formulas, choose the formula that corresponds to the value of cot 4A... Using the half-angle formula, identify a formula for cos (A4)... In ΔDEF if ∠E = 90°, then find the value of sin 2D... In right triangle ABC, if ∠B = 90°, then find the value of cos2(C2)... Which one of these represents sin 2θ in terms of tan θ?.. Choose a formula that represents cos 2θ in terms of tan θ... Simplify 1-cos2Asin2A. .. The value of cos215° - sin215° = .. Use half-angle formula to find the value of tan 15°... Simplify: (tan θ + cot θ) sin 2θ.. Find the value of (sin A + cos A)2 in terms of sin 2A... Find the value of (cos4A - sin4A) in terms of cos 2A... (cot θ - tan θ) = .. Tony wanted to buy a watch which costs $76. He saves $6 on the first day. Each succeeding .. George is a fruit seller. Each day he sells 11 fruits more than what he sold the previous.. The number of microbes in a certain culture doubles every minute. The initial number of mi.. The number of members of a social organization when it was started in 1990 was 650. If th.. The cost of a T.V is $440 which decreases by $27 each year. Find its value after 8 years.. Frank got a job with a starting salary of $25000 per year and an annual increment of 20%. .. Savings of Ed in this week is 24 quarters. After this, each week he saves 20 quarters mor.. Savings of Katie are as follows. 1 penny on the first day, 3 pennies on the second day, 5 .. A school conducted a science fair. The first best exhibit got a prize money of $1000. The .. Jim is dropped a ball from a height of 140 m, the ball rebounds 512th of its height from .. A pendulum swings a total distance of 126 cm before it comes to rest. The ratio of the len.. A triangle is divided into 4 triangles by joining the mid points of its sides. Each trian.. In an equilateral triangle of side 14 cm, the mid points of the sides are joined to form a.. A square is constructed with a side of length 36 cm. A second square is constructed insid.. John wants to clear a loan of $3600 in 40 annual installments, which form an arithmetic se.. The length of the arc of the swing of a pendulum is 378 mm. If the length of the arc of ea.. 98000 people visited a great museum in a month. If the rate of increase in the number of .. A conference hall has 38 rows of seats. The first row has 22 seats and each successive row.. A balloon is filled with a gas of volume 1800 cm3. It looses one tenth of the volume each .. David started a company to make pens. In the first month 12000 number of pens were produc.. A clock chimes once at 1'o clock, twice at 2'o clock and so on. How many times does the cl.. The population of a state increases at the rate of 10% per year. The population of the sta..
