The lifetime of a light bulb is a random variable with a normal distribution of x = 300 hours, σ = 35 hours.
a) What is the probability that a randomly selected light bulb will have a lifespan of more than 320 hours?
b) Up to what value of L hours can the lamp life be expected to last longer than L hours with a probability of 0.25?

Correct answer:

p =  0.2839
L =  323.6 h

Step-by-step explanation:

μ=300 h σ=35 h  xN(μ,σ) t>320 h  p=0.2839=0.2839
L=323.6=323.6 h

Did you find an error or inaccuracy? Feel free to write us. Thank you!


Tips to related online calculators
Looking for help with calculating arithmetic mean?
Looking for a statistical calculator?
Looking for a standard deviation calculator?
Would you like to compute count of combinations?

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Ball bearings
    normal_d One bearing is selected from the shipment of ball bearings. It is known from previous deliveries that the inner bearing radius can be considered as a normal distribution of N (µ = 0.400, σ2 = 25.10^−6). Calculate the probability that the selected radius w
  • Stoaches
    normal_d Stoaches are fictional creatures distantly related to bigfoot and yeti. Stoach weights are normally distributed, with mean 904g and standard deviation 104g. State the probability that the sample mean of a random sample of 36 stoach weights exceeds 943g. (
  • Life expectancy
    normal_d The life expectancy of batteries has a normal distribution with a mean of 350 minutes and standard deviation of 10 minutes. What the range in minutes 68% of the batteries will last? What is the range in minutes approximately 99.7% of batteries will last?
  • IQ Intelligence quotient
    normal_d Intelligence quotient (IQ) is a standardized score used as the output of standardized intelligence psychological tests to quantify a person's intelligence with the rest of the population (respectively to a given group). Intelligence has an approximately n
  • Suppose 4
    normal_d Suppose that 14% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be
  • Standard deviation
    standard-dev Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
  • Twenty
    lastovicka Twenty swallows sit on a 10 m long telephone cable. Assume that swallows are completely randomly distributed along the line. (a) What is the probability that more than three swallows sit on a randomly selected section of cable 1 m long? (b) What is the pr
  • The raw
    statistics The raw data presented here are the scores (out of 100 marks) of a market survey regarding the acceptability of new product launched by a company for a random sample of 50 respondents: 40 45 41 45 45 30 30 8 48 25 26 9 23 24 26 29 8 40 41 42 39 35 18 25 3
  • Normal Distribution
    normal_d At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5?
  • Three sigma rule
    stromy The height of trees in a given stand is known to be a quantity with a normal probability distribution with a mean value of 15 m and a variance of 5 m2. Determine the interval in which there will be tree heights in such a stand with a probability of 90%
  • Probability of failures
    binomial In certain productions, the probability of failures is 0.01. Calculate the probability that there will be more than one failure among the 100 selected products if we return the selected products to the file after the check.
  • Dataset:
    statistics Dataset: 35 22 18 54 22 46 28 31 43 22 14 17 25 19 33 14. 1 Group the data into a grouped distribution using 6 classes of equal width. 2. Determine the mean, median, and mode using the raw data. 3. Draw an Ogive curve corresponding to the data and use it
  • Assembly time
    mean_normal The assembly time for the toy follows a normal distribution with a mean of 75 minutes and a standard deviation of 9 minutes. The company closes at 5 pm every day. If one starts assembling at 4 pm what is the probability that he will finish before the comp
  • A mountain climber
    rope_normal_stdev A mountain climber plans to buy some rope to use as lifeline. Which of the following would be the better choice? Explain your choice. Rope A: Mean breaking strength:500lb; standard deviation of 100lb Rope B: Mean breaking strength: 500lb; standard deviati
  • A machine
    rods_normal A machine produces steel rods of normally distributed length; the mean length and the standard deviation being 50.0 cm and 0.5 cm respectively. The rods do not conform to safety standards if they are either shorter than 49.1 cm or longer than 50.7 cm in l
  • Performance comparing
    statistics A standardized test was administered to thousands of students with a mean score of 85 and a standard deviation of 8. A random sample of 50 students were given the same test and showed an average score of 83.20. Is there evidence to show that this group ha
  • Sample Proportion
    binomial1 In a California community college, 60% of students will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution. 400 students are randomly selected from the college and 224 of them will