Advertisements
Advertisements
प्रश्न
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 between 65 and 71 inches
Advertisements
उत्तर
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(Between 65 and 71 inches)
P(65 ≤ x ≤ 71)
When x = 65
z = `(65 - 68)/3 = (-3)/3 = - 1`
When x = 71
z = `(71 - 68)/3 = 3/3` = 1
P(65 ≤ x ≤ 71) = P(– 1 < z < 1)
= P(– 1 < z < 0) + P(0 < z < 1)
= P(0 < z < 1) + P(0 < z < 1)
= 2 × [P(0 < z < 1)]
= 2 × 0.3413
= 0.6826
∴ Number of students whose height between 65 and 7 inches
= 0.6826 × 500
= 341.3
= 342 .......(approximately)
APPEARS IN
संबंधित प्रश्न
Mention the properties of binomial distribution.
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that atleast three of the travelers have a laptop?
An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be three successes
A car hiring firm has two cars. The demand for cars on each day is distributed as a Posison variate, with mean 1.5. Calculate the proportion of days on which some demand is refused
Define Normal distribution
In a test on 2,000 electric bulbs, it was found that bulbs of a particular make, was normally distributed with an average life of 2,040 hours and standard deviation of 60 hours. Estimate the number of bulbs likely to burn for more 1,920 hours but less than 2,100 hours
Choose the correct alternative:
If Z is a standard normal variate, the proportion of items lying between Z = – 0.5 and Z = – 3.0 is
Choose the correct alternative:
The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?
Choose the correct alternative:
Monthly expenditure on their credit cards, by credit cardholders from a certain bank, follows a normal distribution with a mean of ₹ 1,295.00 and a standard deviation of ₹ 750.00. What proportion of credit cardholders spend more than ₹ 1,500.00 on their credit cards per month?
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn between $45,000 and $65,000?
