The marks in Statistics of students studying in a class follows normal distribution. The mean of this distribution is $65$ marks and standard deviation is $5$ marks. If $10$ students have scored less than $60$ marks, estimate the total number of students.
According to the survey of a company manufacturing school uniforms, the average waist size of students of a school is $66 cm$ and its standard deviation is $5\ cm$. What will be the percentage of students having waist size $(1)$ more than $72\ cm ?\ (2)$ less than $62 cm$ ? $($Use normal distribution.$)$
The monthly personal expense of $500$ students residing in a $(₹ 500$. If the monthly expense follows normal distribution, how many students will have monthly expense$)\ (1 )$ between $₹\ 4300$ and $₹\ 6100\ ?\ (2)$ more than $₹\ (5200) ?$
The mean life of bulbs of a company is $1500$ hours and the
standard deviation is $160$ hours. Find the probability that a
bulb selected from the production of this company has
life
$(1)$ more than $1780$ hours
$(2)$ from $1364$ hours to $1780$ hours
$($The life of bulbs follows normal distribution$.)$
If $P\left(z \leq z_1\right)=0.3085$ and $P\left(z_1 \leq z \leq z_2\right)=0.4796$ for a standard normal variable $Z$, find the values of $z_1$ and $z_2$.
If the $z$ - score of the observations $34$ and $62$ of a normal variable $X$ are $-2$ and $1.5$ respectively, find the mean and standard deviation of the variable.