Maths · Probability: Probability of an event, addition and multiplication theorems of probability
The length of life of an instrument produced by a machine has a normal distribut
The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last less than 7 months.
- A. 0.2316
- B. 0.0062
- C. 0.0072
- D. 0.2136
Step-by-step solution
Let X be the lifetime in months, X ~ N(12, 2^2). Compute z-score: z = (7 - 12)/2 = -2.5. Using standard normal table, P(Z < -2.5) = 1 - P(Z < 2.5) = 1 - 0.9938 = 0.0062.
Related MCQs
- The probability of an even happens in one trial of an experiment is Three independent trials of the experiments are performed. Find the prob…
- What is the probability of selecting two spade cards from a pack of 52 cards?…
- If =\boldsymbol{P}(\boldsymbol{B}), \) then the two events and are -…
- If and are independent events such that <\mathbf{1}, \mathbf{0}<\boldsymbol{P}(\boldsymbol{B})<\mathbf{1}, \) then This question has multipl…
- Let and be two events such that =\frac{1}{6}, P(A \cap B)=\frac{1}{4} \) and =\frac{1}{4}, \) where stands for the complement of the event A…