\( 1 \leftarrow \) A set of data items is normally distributed with a mean of 70 and a standard deviation of 5 . Convert 70 to a z-score. \( \mathrm{z}_{70}=\square \) (Do not round until the final answer. Then round to the nearest hundredth as needed.)

a) Find the critical \( \chi^{2}- \) value for a left-tailed test when \( n=11 \) and \( \alpha=0.01 \). marks] b) Find the critical \( \chi^{2}- \) value for a two-tailed test when \( n=9 \) and \( \alpha=0.05 \). marks]

4 If the point \( (30,50) \) is the point of intersection of the ascending and descending curves, then the sum of its frequency equals \( \begin{array}{llll}\text { (a) } 30 & \text { (b) } 50 & \text { (c) } 60 & \text { (d) } 100\end{array} \)

Four scenarios of statistical studies are given below. Decide which study uses a population parameter. Answer 1000 of the 1883 participants in last year's Ironman in Kona, Hawail were interviewed. \( 68 \% \) of those interviewed said they became interested in triathlons after first ofmpeting in marathons. 351 dog owners who were surveyed, 70 reported owning two dogs. Parkland Hospital performs 15,000 births a year. Of 1000 subjects in a study on multiple births, 38 gave birth to twins. in \( 2001.78 \% \) of children diagnosed with cancer were in remission after five years, and this number is improving.

In how many ways can a committee of 5 students be formed from 10 students?

A water bottling facility has a mean bottling rate of 33.5 thousand bottles per hour with a standard deviation of 1.92 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 26.2 thousand bottles per hour with a standard deviation of 1.42 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 36.8 thousand bottles of water, and the cola bottling facility bottled 28.4 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer