Assume the random variable \( X \) is normally distributed with mean \( \mu=50 \) and standard deviation \( \sigma=7 \). Find the 97 th percentile. The 97 th percentile is (Round to two decimal places as needed.)

2. Find the following confidence intervals for the variance and the standard deviation for the Price in dollars of an adult single - day skitift ticket. The data represents a selected sample of nationwide ski reports. Assume the variable is normally distributed.

(b) Suppose a random sample of 51 human pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of \( \overline{\mathrm{x}} \) is \( \square \) with \( \mu_{\bar{x}}=\square \) and \( \sigma_{\overline{\mathrm{x}}}=\square \). (Round to four decimal places as needed.)

he acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 40 ten-gram portions of the food ite 4.4 insect fragments per ten-gram portion. Complete parts (a) through (c). A. The sampling distribution is approximately normal because the population is normally distributed and the sample size is large enough. B. The sampling distribution is assumed to be approximately normal. C. The sampling distribution is approximately normal because the sample size is large enough. D. The sampling distribution is approximately normal because the population is normally distributed. (b) What is the mean and standard deviation of the sampling distribution of \( \bar{x} \) assuming \( \mu=4 \) and \( \sigma=\sqrt{4} \) ? H- \( =\square \) (Type an integer or a decimal rounded to three decimal places as needed.)

A random sample of 100 claim amounts \( x_{1}, x_{2}, \ldots, x_{100} \) is obrerved from a Weibull distribution with parameter \( y=2 \), where \( c \) is unknoun. For these data: \( \sum x_{i}=487,926 \quad \sum x_{i}^{2}=976,444,000 \quad \) Median \( =4,500 \) a) Show that the maximum likelihood estimator for \( c \) is given by \( \hat{c}=\frac{n}{\sum x_{i}^{2}} \) b) Estimate the value of \( c \) using the method of moments c) Calculate the method of percentiles estimate of \( c \)

5) Determine whether a correlation between the number of new covid cases and percentage of people wearing masta. Doplain your reasoning. of new covid cases and percentage of people wearing masts. Explain your reasoning.