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Statistics 2 Marks Each

PART 2 : NORMAL DISTRIBUTION · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 9 questions.

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2 Marks Each

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9 questions · timed · auto-graded

Question 12 Marks
The normal distribution of marks of a group of students is $N(40,64)$. Find the probability that the marks of a student of this group will be more than $36 .$
Answer
$0.6915$
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Question 22 Marks
The average monthly salary of workers in a factory is $₹ 7,000$ and its standard deviation is $₹ 400$. If the distribution of monthly salary of workers is normal, find the probability that a worker in this factory earns less than $₹ 8,000$.
Answer
$0.9938$
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Question 32 Marks
If $P\left(-1 \leq z \leq z_1\right)=0.823$ for a $z$ - score $z_1$ of the standard normal variable, find the value of $z_1$.
Answer
$2.09$
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Question 42 Marks
If $P\left(1.1 \leq z \leq z_1\right)=0.125$ for the standard normal variable $Z$, find the value of $z_1$.
Answer
$2.3$
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Question 62 Marks
If the probability of $z$ - score lying from $-z_1$ to $z_1$ is $0.39$, find the value of $z_1$.
Answer
$0.51$
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Question 72 Marks
If the difference between two extreme quartiles of a normal variable is $20 ,$ find the approximate value of its standard deviation.
Answer
$15$
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Question 82 Marks
The value of the third quartile of a normal variable is $60.5$. If its standard deviation is $18 ,$ find the value of its first quartile.
Answer
$36.5$
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Question 92 Marks
The probability mass function of a normal variable is as follows: $ f(x)=\frac{1}{\sqrt{18 \pi}} e^{\frac{-(x-12)^2}{18}}, \quad-\infty$
Answer
$(9,15)$
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2 Marks Each - Statistics STD 12 Commerce Questions - Vidyadip