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 between 65 and 71 inches
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(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
RELATED QUESTIONS
In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that atleast two-third have newspaper reading habit
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 3 will have a laptop?
The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? [Given e–2.8 = 0.06]
The average number of phone calls per minute into the switchboard of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be exactly 3 calls
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be at most 3 accidents
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 than 2,150 hours
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 less than or equal to 64 inches
Choose the correct alternative:
In a parametric distribution the mean is equal to variance is
Choose the correct alternative:
The weights of newborn human babies are normally distributed with a mean of 3.2 kg and a standard deviation of 1.1 kg. What is the probability that a randomly selected newborn baby weight less than 2.0 kg?
Choose the correct alternative:
If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?
