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
Define Binomial distribution
Derive the mean and variance 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 the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more?
A car hiring firm has two cars. The demand for cars on each day is distributed as a Poison variate, with mean 1.5. Calculate the proportion of days on which neither car is used
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?
Choose the correct alternative:
If P(Z > z) = 0.5832 what is the value of z (z has a standard normal distribution)?
Choose the correct alternative:
In a binomial distribution, the probability of success is twice as that of failure. Then out of 4 trials, the probability of no success is
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Raghul takes the test and scores 585. Will he be admitted to this university?
