In a class, there are 750 learners in 1st year, 420 learners in 2 nd year. Draw a pie graph to represent the numbers of learners in these groups.

A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 11 doors is taken, and it is found that they have a mean of 2070 millimeters with a variance of 400 . Assume the population is normally distributed. Is there evidence at the 0.05 level that the doors are too long and need to be trimmed? Step 1 of \( 6: \) State the null and alternative hypotheses. Answer 2 Points

A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 11 doors is taken, and it is found that they have a mean of 2070 millimeters with a variance of 400 . Assume the population is normally distributed. Is there evidence at the 0.05 level that the doors are too long and need to be trimmed? Step 3 of 6 : Specify if the test is one-tailed or two-tailed. Answer 2 Points

5. En una muestra al azar de 600 mujeres, 300 indican que están a favor de los bonos estudiantiles. Determinar un intervalo de confianza del \( 90 \% \) para la proporción de mujeres que favorecen esta ayuda.

15. यदि \( n(\mathrm{~A})=5 \) एवं \( n(\mathrm{~B})=2 \), तो \( n(\mathrm{~A} \cap \mathrm{~B}) \) में अधिकतम कितने सदस्य होंगे? \( \begin{array}{ll}\text { (1) } 2 & \text { (2) } 5 \\ \text { (3) } 7 & \text { (4) } 3\end{array} \)

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 439 gram setting. Is there sufficient evidence at the 0.05 level that the bags are underfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scehario. Answer 2 Points