English
Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

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 deviatio

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

Let x be the random variable have long the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second

µ = 16,28 and σ = 0.12

The standard normal variate

z = `(x - mu)/sigma = (x - 16.28)/0.12` = 1

P(Less than 16.35 seconds) = P(x < 16.35)

When x = 16.35

z = `(16.35 - 16.28)/0.12 = 0.17/0.12` = 0.583

P(X < 16.35) = P(Z < 0.583)

= P(`-oo` < z < 0) + P(0 < z < 0.583)

= 0.5 + 0.2190

= 0.7190

shaalaa.com
Distribution
  Is there an error in this question or solution?
Chapter 7: Probability Distributions - Exercise 7.3 [Page 168]

APPEARS IN

Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 7 Probability Distributions
Exercise 7.3 | Q 9 | Page 168

RELATED QUESTIONS

Mention the properties of binomial distribution.


An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be at least three successes


Define Poisson distribution


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


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 atleast 5 calls


Write down the conditions in which the Normal distribution is a limiting case of binomial distribution


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 takes at most 500 days to complete the flyover?


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:

A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?


A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain at least 2 rejects?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×