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25 questions · timed · auto-graded

MCQ 21 Mark
The mean and standard deviation of a normal variable $X$ are $20.5$ and $5$ respectively. Find $P(0 \leq x \leq 26.5)$.
  • A
    $0.1151$
  • B
    $0.8849$
  • $0.3849$
  • D
    $0.7698$
Answer
Correct option: C.
$0.3849$
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MCQ 31 Mark
If $P\left(0 \leq z \leq z_1\right)=0.377$ for the standard normal variable $Z$, state the value of $P (-\infty)$
  • $0.123$
  • B
    $0.877$
  • C
    $0.754$
  • D
    $0.377$
Answer
Correct option: A.
$0.123$
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MCQ 51 Mark
What will be the value of $P(z=1.5)$ for the standard normal variable $Z$ ?
  • A
    $0.4332$
  • B
    $0.9332$
  • $0$
  • D
    $0.0668$
Answer
Correct option: C.
$0$
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MCQ 61 Mark
The mean of a normal variable $X$ is $18 .$ If the $z-\operatorname{score}$ for $x=21$ has value $2 ,$ what will be the standard deviation of the distribution ?
  • $1.5$
  • B
    $2.25$
  • C
    $3$
  • D
    $9$
Answer
Correct option: A.
$1.5$
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MCQ 71 Mark
The variance of a normal variable $X$ is $9 .$ If the $z$ - score for $x=15.5$ has value $-1.5$, what will be the mean of the distribution ?
  • A
    $2$
  • $20$
  • C
    $29$
  • D
    $11$
Answer
Correct option: B.
$20$
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MCQ 81 Mark
The mean and variance of a nomal variable $X$ are $30$ and $16$ respectively. What will be the $z$ - score for $x=26\ ?$
  • $-1$
  • B
    $1$
  • C
    $2$
  • D
    $-0.25$
Answer
Correct option: A.
$-1$
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MCQ 91 Mark
If the distribution of a normal variable is $N(15,9)$, which of the following interval will include its central $95.45 \%$ observations ?
  • A
    $(12,18)$
  • B
    $(6,24)$
  • C
    $(10.5,19.5)$
  • $(9,21)$
Answer
Correct option: D.
$(9,21)$
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MCQ 101 Mark
What is the percentage of observations of normal distribution to the right of the perpendicular drawn at $x=\mu+\sigma$ ?
  • A
    $84.13$
  • B
    $68.26$
  • $15.87$
  • D
    $34.13$
Answer
Correct option: C.
$15.87$
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MCQ 111 Mark
Generally, what are limits that include the central $95.45 \%$ observations of a normal distribution ?
  • A
    $\mu \pm \sigma$
  • $\mu \pm 2 \sigma$
  • C
    $\mu \pm 1.96^ \circ$
  • D
    $\mu \pm 3 \sigma$
Answer
Correct option: B.
$\mu \pm 2 \sigma$
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MCQ 121 Mark
Which of the following is the interval for the central $68.26 \%$ observations of standard nomal variable ?
  • $(-1,1)$
  • B
    $(0,1)$
  • C
    $(-1,0)$
  • D
    $(1, \infty)$
Answer
Correct option: A.
$(-1,1)$
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MCQ 131 Mark
What will be the approximate value of mean deviation of standard normal variable ?
  • A
    $-0.8$
  • $0.8$
  • C
    $1$
  • D
    $0.67$
Answer
Correct option: B.
$0.8$
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MCQ 141 Mark
What is the standard deviation of a standard normal variable ?
  • A
    $-1$
  • B
    $0$
  • $1$
  • D
    $2$
Answer
Correct option: C.
$1$
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MCQ 151 Mark
The variance of a normal variable is $81 .$ What will be the approximate value of its quartile deviation?
  • $6$
  • B
    $7.2$
  • C
    $54$
  • D
    $13.5$
Answer
Correct option: A.
$6$
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MCQ 161 Mark
What will be the approximate value of mean deviation for a normal distribution $N(20,225)$ ?
  • A
    $10$
  • $12$
  • C
    $16$
  • D
    $18.75$
Answer
Correct option: B.
$12$
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MCQ 171 Mark
What is the approximate value of $Q_3$ for the normal distribution $N\left(\mu, \sigma^2\right)$ ?
  • A
    $\mu+0.657 \sigma$
  • B
    $\mu-0,657 \sigma$
  • $\mu+0.675 \sigma$
  • D
    $\mu-0.675 \sigma$
Answer
Correct option: C.
$\mu+0.675 \sigma$
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MCQ 181 Mark
If the two extreme quartiles of a normal variable are $10$ and $40.$ What will be its mean?
  • A
    $30$
  • B
    $15$
  • C
    $50$
  • $25$
Answer
Correct option: D.
$25$
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MCQ 191 Mark
Which of the following can be the probability density function for a normal variable $X$ ?
  • $f(x)=\frac{1}{\sqrt{32 \pi}} e^{\frac{1}{2}\left(\frac{1-10}{4}\right)^2}$
  • B
    $f(x)=\frac{1}{\sqrt{16 \pi}} e^{\frac{1}{2}\left(\frac{x-10}{4}\right)^2}$
  • C
    $f(x)=\frac{1}{\sqrt{4 \pi}} e^{\frac{1}{2}\left(\frac{x-10}{4}\right)^2}$
  • D
    $f(x)=\frac{1}{4 \sqrt{\pi}} e^{\frac{-1}{2}\left(\frac{x-10}{4}\right)^2}$
Answer
Correct option: A.
$f(x)=\frac{1}{\sqrt{32 \pi}} e^{\frac{1}{2}\left(\frac{1-10}{4}\right)^2}$
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MCQ 201 Mark
Which of the following is true for a normal variable?
  • A
    $Q_3+Q_1=\mu$
  • $Q_3+Q_1=2 \mu$
  • C
    $Q_3-Q_1=\mu$
  • D
    $Q_3-Q_1=2 \mu$
Answer
Correct option: B.
$Q_3+Q_1=2 \mu$
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MCQ 211 Mark
What will be the median of a normal variable following normal distribution $N(30,100)$ ?
  • A
    $10$
  • $30$
  • C
    $\sqrt{30}$
  • D
    $\sqrt{10}$
Answer
Correct option: B.
$30$
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MCQ 221 Mark
The probability curve of a normal variable $X$ is symmetric around $x=34$. What would be its mode ?
  • A
    $0$
  • B
    $43$
  • $34$
  • D
    $-34$
Answer
Correct option: C.
$34$
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MCQ 231 Mark
Which value of normal variable $X$ divides the area under the normal curve in two equal parts?
  • A
    $x=\sigma$
  • $x=\mu$
  • C
    $x=\sigma^2$
  • D
    $x=0$
Answer
Correct option: B.
$x=\mu$
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MCQ 241 Mark
What is the type of curve for normal distribution ?
  • A
    Positively skewed
  • B
    Negatively skewed
  • Symmetric
  • D
    Nothing can be said
Answer
Correct option: C.
Symmetric
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MCQ 251 Mark
Which of the following is true for the standard normal variable $Z$ ?
  • A
    $0 \leq z<\infty$
  • B
    $-3.5 \leq z \leq 3.5$
  • C
    $0>\infty$
  • $-\infty$
Answer
Correct option: D.
$-\infty$
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MCQ - Statistics STD 12 Commerce Questions - Vidyadip