Statistics Questions & Answers

Cuts Pizza is a large restaurant chain. After paying for a meal at Cuts Pizza, customers are asked to rate the quality of the food as rating of 1 means "not good" and 5 means "excellent". The customers' ratings have a population mean of \( \mu=4.60 \), with a standar Suppose that we will take a random sample of \( n=10 \) customers' ratings. Let \( \bar{x} \) represent the sample mean of the 10 customers' ra distribution of the sample mean \( \bar{x} \). Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if need (a) Find \( \mu_{-} \)(the mean of the sampling distribution of the sample mean). (b) Find \( \sigma_{-} \)(the standard deviation of the sampling distribution of the sample mean). \( \sigma_{-}=\square \)

Suppose the lengths of human pregnancies are normally distributed with \( \mu=266 \) days and \( \sigma=16 \) days. Complete parts (a) and (b) bel (a) The figure to the right represents the normal curve with \( \mu=266 \) days and \( \sigma=16 \) days. The area to the left of \( X=250 \) is 0.1587 . Pro Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete) (Type integers or decimals.) A. The proportion of human pregnancies that last more than \( \square \) days is \( \square \). B. The proportion of human pregnancies that last less than \( \square \) days is \( \square \).

(c) Suppose the area under the normal ourve to the right of \( X=4450 \) is 0.0228 . Provide an interpretation of this result. Select the correct choice below and fil (Type a whole number.) A. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than grams. B. The probability is 0.0228 that the birth weight of a randomly chosen fulliterm baby in this population is less than grams.

The graph of a normal curve is given on the right. Use the graph to identify the values of \( \mu \) and \( \sigma \), \( \mu=\square \)

There is a weekend fishing competition that Alan participates in each year. There are several other fishing boats that participate in this 0 the competitors, the number of fish caught this year had a mean of 42 fish and a standard deviation of 9 fish. Alan caught 43 fish. (a) Find the \( z \)-score of the number of fish that Alan caught relative to the numbers of fish caught among all the competitors. Round your answer to two decimal places. \( z=\square \) (b) Fill in the blanks to interpret the \( z \)-score of the number of fish that Alan caught. Make sure to express your answer in terms of a positive number of standard deviations. Tish caught among all the competitors.

Which of the following are properties of the normal curve? Select all that apply. \( \square \) A. The graph of a normal curve is symmetric. \( \square \) B. The graph of a normal curve is skewed right. \( \square \) C. The area under the normal curve to the right of the mean is 0.5 \( \square \) D. The high point is located at the value of the mean. \( \square \) E. The high point is located at the value of the standard deviation. \( \square \) F. The area under the normal curve to the right of the mean is 1 .

Which of the following are properties of the normal curve? Select all that apply A. The graph of a normal curve is skewed right. B. The high point is located at the value of the standard deviation. C. The area under the normal curve to the right of the mean is 0.5 . D. The high point is located at the value of the mean. E. The graph of a normal curve is symmetric.

1. Suponga que seleccionó una muestra aleatoria de \( n-7 \) mediciones de una distribución normal Compare los valores-z normal estándar con los correspondientes valores-t necesarios para construir los siguientes intervalos de confianza Utilice un software, tablas o el applet sobre distribuciones de probabilidad a. Intervalo de confianza de \( 80 \% \) b. Intervalo de confianza de \( 90 \% \) c. Intervalo de confianza de \( 95 \% \) d. Intervalo de confianza de \( 98 \% \) e. Intervalo de confianza de \( 99 \% \)

42. En un conjunto de datos, se dice que un dato es atíico cuando es menor que \( Q_{1}-\frac{3}{2} R \) o mayor que \( Q_{3}+\frac{3}{2} R \), tal que \( Q_{1} \) es el primer cuartil de la distribución, \( Q_{3} \) es el tercer cuartily \( R \) es el rango intercuartilico. Considera un conjunto de datos con primer cuartil 20 y tercer cuartil 40 . Si los mayores datos de la distribución son \( 60,65,72 \) y 78, ¿cuántos de ellos son datos atípicos? A) 1 B) 2 C) 3 D) 4

62. Los sigulentes datos corresponden a la masa de los tomates cosechados en un huerto de una escuela: \( 75 \mathrm{~g}, 77 \mathrm{~g}, 84 \mathrm{~g}, 98 \mathrm{~g}, 101 \mathrm{~g}, 116 \mathrm{~g}, 129 \mathrm{~g}, 132 \mathrm{~g} \). \( 145 \mathrm{~g}, 152 \mathrm{~g}, 163 \mathrm{~g} \) y 176 g . ¿Cuál de los siguientes percentiles supera los 100 g ? A) 10 B) 20 C) 30 D) 40