In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 20 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of \( 9.02 \mathrm{~cm}^{3} \). An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and \( \bar{x}=8.14 \mathrm{~cm}^{3} \) and \( \mathrm{s}=0.7 \mathrm{~cm}^{3} \). Conduct the appropriate test at the \( \alpha=0.01 \) level of significance. \( \mathrm{H}_{0}: \mu=9.02 \) \( \mathrm{H}_{1}: \mu<9.02 \) (Type integers or decimals. Do not round.) Identify the \( t \)-statistic. \( t_{0}=\square \) (Round to two decimal places as needed.)

Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1 . If \( P(-b<z<b)=0.7944 \), find \( b \). \( b=\square \) Submit Question

A population of values has a normal distribution with \( \mu=42.8 \) and \( \sigma=88.4 \). You intend to draw a random sample of size \( n=220 \). Find the probability that a single randomly selected value is less than 36.8 . \( P(x<36.8)= \) Find the probability that a sample of size \( n=220 \) is randomly selected with a mean less that 36.8 . \( P(\bar{x}<36.8)= \) Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact \( z \) - scores or \( z \)-scores rounded to 3 decimal places are accepted.

pulation of values has a normal distribution with \( \mu=54.8 \) and \( \sigma=41.4 \). You intend to draw a dom sample of size \( n=206 \). \( >52.2)=\square \) the probability that a single randomly selected value is greater than 52.2 . \( > \) the probability that a sample of size \( n=206 \) is randomly selected with a mean greater than 52.2 . \( >52.2)=\square \) er your answers as numbers accurate to 4 decimal places. Answers obtained using exact \( z \)-scores or \( z \) - res rounded to 3 decimal places are accepted.

CNNBC recently reported that the mean annual cost of auto insurance is 1047 dollars. Assur the standard deviation is 291 dollars. You take a simple random sample of 64 auto insurance policies. Find the probability that a single randomly selected value is less than 991 dollars. \( P(x<991)= \) Find the probability that a sample of size \( n=64 \) is randomly selected with a mean less tha 991 dollars. \( P(\bar{x}<991)= \)

A population of values has a normal distribution with \( \mu=116.7 \) and \( \sigma=12.4 \). You intend to draw a random sample of size \( n=151 \). Find the probability that a single randomly selected value is less than 115.5 . \( P(x<115.5)= \) Find the probability that a sample of size \( n=151 \) is randomly selected with a mean less than 115.5 . \( P(\bar{x}<115.5)= \) Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact \( z \)-scores or scores rounded to 3 decimal places are accepted. Submit Question