CA Foundation · Quantitative Aptitude · Theoretical Distributions
In a normal distribution, if the mean is 50 and standard deviation is 10, what is the z-score for a value of 65?
The z-score is 1.5. Using the formula z = (X - mean) / standard deviation, we substitute the given values: (65 - 50) / 10 = 1.5, showing the data point is 1.5 standard deviations above the mean.
- A0.5
- B1.5Correct
- C2.5
- D3.5
Explanation
The z-score formula is z = (X - μ) / σ. Here, z = (65 - 50) / 10 = 15 / 10 = 1.5. This indicates the value is 1.5 standard deviations above the mean. Option 0.5 would result from incorrectly dividing by 30; option 2.5 comes from halving the correct numerator first.
Did you get it right without looking?
One question tells you little. A timed set on Theoretical Distributions shows your real accuracy, how long you take and where you lose marks.
More Theoretical Distributions questions
- A continuous random variable X follows a normal distribution with mean 50 and standard deviation 10. If Z represents the standardised normal…
- A quality control process inspects batches of electronic components. The inspection follows a binomial distribution where each component has…
- A quality inspector at a Surat factory tests 5 independently made items, each with a 0.4 chance of being defective. What is the probability …
- A pharmaceutical company observes that medication prescriptions follow a binomial distribution where the probability of a patient showing im…
- A factory produces ball bearings with a mean diameter of 8 mm and standard deviation of 0.2 mm, normally distributed. If the specification a…
- The weights of packets filled by a machine in Surat follow a normal distribution with standard deviation 15 grams. Using the relationship be…