Find the area under the standard normal curve to the left of <\/p>\n\n\n\n
a. z = 2.56 <\/p>\n\n\n\n
b. z = 0.53 <\/p>\n\n\n\n
c. z = -0.94 <\/p>\n\n\n\n
d. z = -1.30<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n Here are the areas under the standard normal curve to the left of each given z-value:<\/p>\n\n\n\n a. For z = 2.56 b. For z = 0.53 c. For z = -0.94 d. For z = -1.30 The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. The total area under the curve is equal to 1, which corresponds to 100% probability. The area to the left of a specific z-value represents the cumulative probability that a randomly selected value from the distribution is less than that z-value.<\/p>\n\n\n\n To find these areas, a standard normal table or a calculator with the cumulative distribution function (CDF) for the standard normal distribution is used. This function gives the probability that a value is less than or equal to a given z-score.<\/p>\n\n\n\n For positive z-values (like 2.56 and 0.53), the area to the left is greater than 0.5 because the mean (0) divides the distribution into two equal halves. As the z-value increases positively, the cumulative area approaches 1.<\/p>\n\n\n\n For negative z-values (like -0.94 and -1.30), the area to the left is less than 0.5. This is because these values lie to the left of the mean, so the cumulative probability is smaller. As the z-value becomes more negative, the cumulative area approaches 0.<\/p>\n\n\n\n The exact values come from either a table or software that calculates the integral of the probability density function from negative infinity up to the z-value. This is important for many statistical analyses, including hypothesis testing and confidence interval construction.<\/p>\n\n\n\n In summary, the area to the left of a z-score tells the likelihood that a standard normal random variable is less than that z-score. These values are essential for interpreting probabilities and making decisions based on normal distributions.<\/p>\n","protected":false},"excerpt":{"rendered":" Find the area under the standard normal curve to the left of a. z = 2.56 b. z = 0.53 c. z = -0.94 d. z = -1.30 The correct answer and explanation is: Here are the areas under the standard normal curve to the left of each given z-value: a. For z = 2.56Area […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-36291","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36291","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=36291"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36291\/revisions"}],"predecessor-version":[{"id":36293,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36291\/revisions\/36293"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=36291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=36291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=36291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Area to the left \u2248 0.9948<\/p>\n\n\n\n
Area to the left \u2248 0.7019<\/p>\n\n\n\n
Area to the left \u2248 0.1736<\/p>\n\n\n\n
Area to the left \u2248 0.0968<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n