Let \( x \) be a continuby nondom variable with probability distribution. \[ P(x)=\left\{\begin{array}{ll}\frac{x}{6}+k \text { if } 0 \leq x \leq 3 \\ 0 \quad & \text { elsewhere }\end{array}\right. \] evaluate \( k \) and find \( P(1 \leqslant x \leqslant 2) \),

Question 19 In a survey, 46\% of Americans say they suffer great stress at least once a week. If three people are selected at random, what is the probability that all three will say that they suffer great stress at least once a week? Add your answer Integer, decimal, or E notation allowed

Question 18 If a person selects a tie from a store with 8 different ties, how many different possibilities are there if they want to rank their top 3 choices? Add your answer Integer, decimal, or E notation allowed

Question 2 The speeds of cars are measured using a radar unit, on a motorway. The speeds are normally distributed with a mean of \( 90 \mathrm{~km} / \mathrm{hr} \) and a standard deviation of \( 10 \mathrm{~km} / \mathrm{hr} \). What is the probability that a car selected at chance moves at more than \( 100 \mathrm{~km} / \mathrm{hr} \) ? Add your answer Integer, decimal, or E notation allowed

Question 1 For some computers, the time period between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. Rohan has one of these computers and needs to know the probability that the time period will be between 50 and 70 hours. Add your answer Integer, decimal, or E notation allowed

Two newspapers \( A \) and \( B \) are published in a city. It is known that \( 25 \% \) of the city populations reads \( A \) and \( 20 \% \) reads \( B \) while \( 8 \% \) reads both \( A \) and \( B \). Further, \( 30 \% \) of those who read \( A \) but not \( B \) look into advertisements and \( 40 \% \) of those who read \( B \) but not \( A \) also look into advertisements, while \( 50 \% \) of those who read both \( A \) and \( B \) look into advertisements. Then the percentage of the population who look into advertisement is [JEE (Main) 2019] \( \begin{array}{ll}\text { (a) } 12.8 & \text { (b) } 13.5 \\ \text { (c) } 13.9 & \text { (d) } 13\end{array} \)