### Distribution of measurement - class-XI

Description: distribution of measurement | |

Number of Questions: 15 | |

Created by: Rachana Sahu | |

Tags: statistics measurements and uncertainties physics maths probability distributions normal distribution probability |

$\sum _{r=1}^{11} r.5^{r} =\dfrac{(43\times 5^{a}+5)}{b}$, then $(a+b)$ is

If $A$ and $B$ are two independent events such that $P(A) = \dfrac{1}{2}$ and $P(B) = \dfrac{2}{3}$, then $P((A \cup B) (A\cup \overline{B})(\overline{A} \cup B))$ has the value equal to

Which of the following is not true regarding the normal distribution?

Which of the following are correct regarding normal distribution curve?

(i) Symmetrical about the line $X=\mu $ (Mean)

(ii) Mean $=$ Median $=$ Mode

(iii) Unimodal

(iv) Points of inflexion are at $X=\mu \pm \sigma $

$X$ is a Normally distributed variable with mean $ = 30$ and standard deviation $ = 4$. Find $P(30 < x<35)$

A large group of students took a test in Physics and the final grades have a mean of $70$ and a standard deviation of $10$. If we can approximate the distribution of these grades by a normal distribution, what percent of the students should fail the test (grades$<60$)?

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.

The scores on standardized admissions test are normally distributed with a mean of $500$ and a standard deviation of $100$. What is the probability that a randomly selected student will score between $400$ and $600$ on the test?

The marks secured by $400$ students in a Mathematics test were normally distributed with mean $65$. If $120$ students got marks above $85$, the number of students securing marks between $45$ and $65$ is

The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000$ and a standard deviation of $20,000$. What percent of people earn between $45,000$ and $65,000$?

The length of similar components produced by a company is approximated by a normal distribution model with a mean of $5$ cm and a standard deviation of $0.02$ cm. If a component is chosen at random, what is the probability that the length of this component is between $4.96$ and $5.04$ cm?

A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of $9$ km/hr and a standard deviation of $10$ km/hr. What is the probability that a car picked at random is travelling at more than $100$ km/hr?