In 1945, an organization asked 1490 randomly sampled American citizens, "Do you think we can develop a way to protect ourselves from atomic bombs in case others tried to use them against us?" with 771 responding yes. Did a majority of the citizens feel the country could develop a way to protect itself from atomic bombs in 1945 ? Use the \( \alpha=0.01 \) level of significance. Use technology to determine the P-value for the test statistic. The P-value is \( \square \). (Round to three decimal places as needed.)

Score on last try: 0 of 1 pts. See Details for more. \( > \) Next question Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1 . If \( P(-b<z<b)=0.6956 \), find \( b \). Submit Question

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. \( P(\bar{x}<991)= \)

Question 12 Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1. \( b=\square<b<b)=0.747 \), find \( b \). Submit Question

population of values has a normal distribution with \( \mu=247.9 \) and \( \sigma=53.8 \). You intend raw a random sample of size \( n=54 \). ind the probability that a single randomly selected value is greater than 269.9 . Find the probability that a sample of size \( n=54 \) is randomly selected with a mean greater than 269.9 . \( P(\bar{x}>269.9)=\square \) 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.