A population of values has a normal distribution with \( \mu=111.2 \) and \( \sigma=39 \). You intend to draw a random sample of size \( n=231 \). Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is between 109.1 and 116.8 . \( P(109.1<X<116.8)=\square \)

Если у вас есть набор данных: (2,3), (4,5), (6,7), как вы можете изобразить эти точки на диаграмме рассеяния?

a. Dans une série statistique, s'il y a autant de don- nées supérieures à 12 que de données inférieures à 12, alors la moyenne est obligatoirement égale à 12 . b. La taille moyenne de n'importe quel groupe d'en- fants mesurant entre \( 1,40 \mathrm{~m} \) et \( 1,50 \mathrm{~m} \) est \( 1,45 \mathrm{~m} \). c. Un magasin a en stock 100 pulls dont \( 10 \% \) sont noirs et 200 tee-shirts dont \( 70 \% \) sont noirs. On peut en conclure que la moitié de ces vêtements sont noirs.

A person's blood glucose level and diabetes are dosely related. Let \( x \) be a random variable measured in milligrams of glucose per deciliter ( \( 1 / 10 \) of a liter) of blood. Suppose that after a 12 -hoi fast, the random variable \( x \) will have a distribution that is approximately normal with mean \( \mu=87 \) and standard deviation \( \sigma=23 \). Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50 ) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) \( x \) is more than 60 (b) \( x \) is less than 110 (c) \( x \) is between 60 and 110 (d) \( x \) is greater than 125 (borderline diabetes starts at 125 )

Question 10 Based on past experience, a bank believes that \( 9 \% \) of the people who receive loans will not make their payments on time. The bank has recently approved 200 loans. a. Write about and check each of the conditions needed in the context of this situation to use the sampling distribution for the proportion of people who will not make their payments on time (Central Limit Theorem). Conditions: \( \begin{array}{l}\text { distritution for the proportion of people who make their payment on } \\ \text { time based on the cental limit theorem. we can proceeds to analyze } \\ \text { the proportion of the sameple that does not make payment on time } \\ \text { using normal approximation methods. } \\ \text { What are the mean and standard deviation of this model? } \\ \text { b. Mean = } 18 \\ \text { c. Standard deviation (accurate to } 4 \text { decimal places) }=4.047 \\ \text { d. What is the probability that } 10 \% \text { or more of these clients will not make timely } \\ \text { payments to } 4 \text { decimal places? } 0.311 \text {. } \\ \text { Question Help: } \square \text { Message instructor } \\ \text { Add Work }\end{array} \).

Question 8 The heights of 10 -year-olds, regardless of gender, closely follow a Normal distribution with a mean of 56 inches and a standard deviation of 5 inches. a. What is the probability that a randomly chosen 10 -year-old is shorter than 48 inches? (Round to 4 decimal places.) b. If the tallest \( 10 \% \) of the class is considered "very tall", what is the height cutoff for "very tall"? (Round to 2 decimal places.) [SAB2]