** GATE 2019 Set-1 **

**1. The lengths of a large stock of titanium rods follow a normal distribution with a mean (𝜇) of 440 mm and a standard deviation (𝜎) of 1 mm. What is the percentage of rods whose lengths lie between 438 mm and 441 mm?**

(A) 81.85%

(B) 68.4%

(C) 99.75%

(D) 86.64%

Answer

Option (A) is correct

**We know that in normal probability distribution, we have **

\(\large \mathrm{Z}=\frac{\mathrm{X}-\mathrm{u}}{\sigma}\)

**lower limit, **

\(\large \mathrm{Z}(\mathrm{x}=438)=\frac{438-440}{1}=-2\)

**Upper limit,**

\(\large \mathrm{Z}(\mathrm{x}=441 \mathrm{})=\frac{441-440}{1}=1\)

**Percentage of rods whose lengths lie between 438 mm and 441 mm.**

\(=P(Z=1)-P(Z=-2)=P(-2<Z<1)\)

**The numerical value of above is nothing but the shaded area in the curve shown below, so we get**

\(\large \approx 0.3415+(0.3415+0.1360)\)

\(\large \approx 0.819=81.9 \%\)

** GATE 2019 Set-2 **

**1. If ***x *is the mean of data 3, *x*, 2 and 4, then the mode is____

Answer

(3 to 3) is correct

**Mean** **x =** \(\large \frac{3+x+2+4}{4}\)

4x = 9 + x

x = 3

The data becomes 3, 3, 2 and 4

**Mode = Maximum times repeated value.**

**Mode = 3**

** GATE 2018 Set-1 **

**1. Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is**

(A) 1/72

(B) 1/55

(C) 1/36

(D) 1/27

Answer

Option (B) is correct

**The probability that all the three balls are red is given by**

\(\large P=\frac{^4C_3}{^{12}C_3}=\frac{\frac{4}{1}}{\frac{12\times11\times10}{3\times2\times1}}\)

\(\large P=\frac{24}{1320}=\frac{1}{55}\)

**2. A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” atleast four times is**

(A) 33.3

(B) 3.33

(C) 0.33

(D) 0.0033

Answer

Option (C) is correct

**Probability of getting 1 in single throw**

\(\large p=\frac{1}{6}\)

**Probability of NOT getting 1 in single throw**

\(\large q=1-\frac{1}{6}=\frac{5}{6}\)

**Probability of getting 1 atleast 4 times in 5 times rolled is given by**

\(=^5C_4\;p^4q^1+^5C_5\;p^5q^0\)

\(\large =5\times\left ( \frac{1}{6} \right )^4\left ( \frac{5}{6} \right )+1\times\left ( \frac{1}{6} \right )^5\)

\(\large =\frac{25}{6^5}+\frac{1}{6^5}\)

\(=0.0033\)

**Now if you are in haste you will put option (D) as correct, but wait it is asking %, hence we have**

\(Ans=0.0033\times100\)

\(Ans=0.33\)

** GATE 2017 Set-1 **

**1. A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ______.**

Answer

(3.5) is correct

The Probabilities corresponding to any of the six outcomes is 1/6

**Number** |
1 |
2 |
3 |
4 |
5 |
6 |

**Probability** |
1/6 |
1/6 |
1/6 |
1/6 |
1/6 |
1/6 |

**Mean value of outcome is given by**

\(\large =\sum _{i=1}^6x_iP_i\)

\(\large =\frac{1+2+3+4+5+6}{6}=3.5\)

** GATE 2017 Set-2 **

**1. The standard deviation of linear dimensions P and Q are 3μm and 4μm respectively. When assembled, the standard deviation (in μm) of the resulting linear dimension (P+Q) is ________**

Answer

(5) is correct

**Variance of P and Q are**

\(V_P=3^2=9\;\mu m\)

\(V_Q=4^2=16\;\mu m\)

**Note**: Variance can be addede.

\(V_{PQ}=9+16=25\)

**Standard deviation is given by**

\(=\sqrt {V_{PQ}}=5\)

**2. Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ____________**

Answer

(0.75) is correct

Sample Space= (H,T) (H,H) (T,T) (T,H)

**Probability of getting atleast 1 head is given by**

\(P=\frac{3}{4}=0.75\)

**3. A sample of 15 data is a follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is**

(A) 4

(B) 13

(C) 17

(D) 20

Answer

Option (C) is correct

**Mode refers to value that appears most frequently in a set of data.**

17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17,3

The data which is repeated for maximum number of times is 17 and frequency = 4

** GATE 2016 Set-1 **

**1. Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is µ. The standard deviation for this distribution is given by**

(A) √µ

(B) µ^{2}

(C) µ

(D) 1/µ

Answer

Option (A) is correct

**Properties of Poisson Distribution**

Mean = Variance = **µ**

Standard deviation = √(Variance) = √µ

** GATE 2016 Set-3 **

**1. The area (in percentage) under standard normal distribution curve of random variable Z within limits from −3 to +3 is __________**

Answer

**(99.7)** is correct

**These are standard results you must remember them.**

** GATE 2015 Set-1 **

**Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?**

(A) I

(B) II

(C) III

(D) IV

Answer

Option (D) is correct

Variance = (Standard deviation)^{2}

Smaller the standard deviation smaller is the variance.

Go To Top

### Discuss below to share your knowledge