Advertisements
Advertisements
Question
If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height greater than 72 inches
Advertisements
Solution
Let x denote the height of a student N = 500; m = 68.0 inches and σ = 3.0 inches the standard normal variate
z = `(x - mu)/sigma = (x - 68)/3`
P(Greater than 72 inches)
P = P(X > 72)
When x = 72
z = `(72 - 68)/3 = 4/3` = 1.33
P(x > 72) = P(z > 1.33)
= 0.5 – 0.4082
= 0.0918
Number of students whose height are greater than 72 inches
= 0.0918 × 500
= 45.9
= 46 ......(approximately)
APPEARS IN
RELATED QUESTIONS
Mention the properties of binomial distribution.
If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are exactly 4 defectives
If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random none will be defective
Among 28 professors of a certain department, 18 drive foreign cars and 10 drive local made cars. If 5 of these professors are selected at random, what is the probability that atleast 3 of them drive foreign cars?
Write the conditions for which the poisson distribution is a limiting case of binomial distribution
Define Standard normal variate
In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints
Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and a standard deviation of 100 labour days. If the company promises to construct the flyover in 450 days or less and agree to pay a penalty of ₹ 10,000 for each labour day spent in excess of 450. What is the probability that the company pay a penalty of at least ₹ 2,00,000?
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time. Between 20 and 22 hours?
X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(30 < X < 35)
